# Tommaso RuggeriUniversity of Bologna | UNIBO · Department of Mathematics MAT

Tommaso Ruggeri

Full Professor

## About

361

Publications

13,380

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6,874

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Citations since 2016

Introduction

My work is mainly devoted on non-linear wave propagation for hyperbolic systems (symmetric systems, shock waves, ...)
and Non-Equilibrium Thermodynamics.
In particular classical and relativistic Rational Extended Thermodynamics and the relation between Continuum Mechanics and the Kinetic Theory.

Additional affiliations

March 2013 - April 2013

January 2008 - February 2008

January 2008 - February 2008

## Publications

Publications (361)

The difference in the theoretical structure between monatomic and polyatomic gases in highly nonequilibrium states is discussed from the viewpoint of molecular extended thermodynamics (MET) of rarefied gases, which is free from the local equilibrium assumption. The MET theories of these two types of gases are based on the moment balance equations w...

We present a thermodynamically consistent particle (TCP) model motivated by the theory of multi-temperature mixture of fluids in the case of spatially homogeneous processes. The proposed model incorporates the Cucker-Smale (C-S) type flocking model as its isothermal approximation. However, it is more complex than the C-S model, because the mutual i...

The goal of the present paper is to construct a relativistic extended thermodynamics (ET) theory of rarefied polyatomic gases. This is achieved by adopting the closure procedure for the generalized moments of a distribution function that, as in the classical case, depends on an additional continuous variable representing the energy of the internal...

We present an extended thermodynamics (ET) theory of dissipative dense gases. In particular, we study the ET theory with six fields, where we neglect shear viscosity and heat conductivity. We postulate a simple principle of duality between rarefied and dense gases. This principle is based on the microscopic analysis of the energy exchange between d...

The fourth-gradient model for fluids—associated with an extended molecular mean-field theory of capillarity—is considered. By producing fluctuations of density near the critical point like in computational molecular dynamics, the model is more realistic and richer than van der Waals’ one and other models associated with a second order expansion. Th...

È dedotta la legge secondo la quale si trasforma, al variare dell’osservatore, la derivata temporale di un generico vettore e vengono introdotte e dimostrate le relazioni che descrivono i cambiamenti di velocità, accelerazione e velocità angolare: Teorema di Galileo, di Coriolis e legge di composizione delle velocità angolari.

Le leggi della statica, che garantiscono l’equilibrio di un punto o di un sistema, sono enunciate e commentate. Si deducono le equazioni cardinali della statica e si enuncia il principio dei lavori virtuali per sistemi soggetti a vincoli ideali e, nel caso di forze conservative, del principio di stazionarietà del potenziale. Si discutono le leggi d...

Sono introdotte le proprietà caratteristiche dei moti rigidi e gli angoli di Eulero. Il concetto di velocità angolare è dedotto per mezzo del Teorema di Poisson e si classificano i moti rigidi più significativi. Il concetto di atto di moto viene illustrato e si dimostra il Teorema di Mozzi. Le leggi di distribuzione delle velocità e delle acceleraz...

Le equazioni cardinali che governano il moto dei sistemi sono enunciate e dedotte. Il teorema dell’energia cinetica e il teorema di moto del baricentro sono dimostrati e, nelle opportune ipotesi, è anche dedotto il teorema di conservazione dell’energia meccanica.

Le quantità meccaniche fondamentali associate al moto di un sistema discreto o continuo di punti materiali sono definite e discusse: quantità di moto, momento delle quantità di moto, energia cinetica. È dimostrato il teorema della quantità di moto. Si deduce l’espressione del momento delle quantità di moto per un sistema con atto di moto rigido e i...

A partire dal principio di D’Alembert si deduce l’equazione simbolica della dinamica, valida per sistemi soggetti a vincoli ideali. Si mostra come, nel caso di vincoli olonomi, da questa si deducano le equazioni di Lagrange nelle due forme, non conservativa e conservativa. Si introducono i momenti cinetici associati alle coordinate libere e si most...

Il concetto di forza applicata a un punto materiale è illustrato, insieme alle quantità ad esso associate di lavoro e potenza, sia effettivi che virtuali. Si introducono forze posizionali e conservative, insieme a potenziale ed energia potenziale. Risultante e momento di un sistema di forze sono definiti e sono dedotte le loro proprietà e i princip...

Le Leggi di Newton vengono enunciate e commentate e se ne mostrano le conseguenze per il calcolo del moto di un punto e di un sistema di punti. Si dimostra che risultante e momento delle forze interne sono sempre nulli. Il postulato delle reazioni vincolari permette di dedurre l’espressione delle reazioni vincolari nel caso di vincoli ideali, che v...

Il moto di un punto nello spazio Euclideo è descritto assegnandone la posizione in funzione del tempo e sono definite velocità e accelerazione. Si mostra che assegnare il moto equivale a conoscere l’equazione della traiettoria e la legge oraria. Il calcolo delle componenti di velocità e accelerazione secondo la terna intrinseca della traiettoria pr...

Vengono classificati i vincoli illustrandoli con molti esempi: vincoli fissi e mobili, olonomi e anolonomi, bilateri e unilateri, esterni e interni. Le coordinate libere, i gradi di libertà, gli spostamenti infinitesimi e virtuali, insieme alle velocità effettive e virtuali, sono presentati, definiti e illustrati anche per mezzo di numerosi esempi,...

In questo capitolo si applicano le leggi della statica ai sistemi continui monodimensionali, quali fili e aste. Si introduce il concetto di azione interna: sforzo assiale e di taglio, momento flettente e torcente. Si deducono le equazioni indefinite di equilibrio in forma integrale e locale. Nel caso di fili, definiti come corpi monodimensionali pe...

Si mostra come per applicare le leggi delle Meccanica in un sistema di riferimento non inerziale sia necessario introdurre le forze apparenti: forza di trascinamento e forza di Coriolis, deducendone le proprietà. In particolare si mostra come si possano calcolare i loro risultanti e, nel caso in cui la forza di trascinamento si riduca alla forza ce...

Il problema della determinazione del moto di un punto, libero o vincolato, è l’argomento di questo capitolo. Si deduce e discute l’equazione pura di moto per un punto vincolato a una traiettoria prestabilita, con vincolo ideale o scabro. L’importante esempio del punto soggetto a una forza elastica, anche in presenza di una dissipazione viscosa o di...

Si introducono i concetti di centro di massa o baricentro e di momento d’inerzia rispetto a un asse, per distribuzioni discrete e continue di punti materiali. Le loro proprietà principali sono dedotte e illustrate per mezzo di numerosi esempi. È definita la matrice di inerzia, insieme all’ellissoide d’inerzia, e ne è mostrato l’utilizzo per il calc...

La discussione delle equazioni di moto di un corpo rigido, sia libero che vincolato, viene presentata in questo capitolo. Si dimostra che le equazioni cardinali sono necessarie e sufficienti per determinare il moto e, ponendosi nel caso di un corpo rigido con un punto fisso, si deducono le equazioni di Eulero. Il fenomeno delle rotazioni permanenti...

A relativistic version of the Kinetic Theory for polyatomic gas is considered and a new hierarchy of moments that takes into account the total energy composed by the rest energy and the energy of the molecular internal modes is presented. In the first part, we prove via classical limit that the truncated system of moments dictates a precise hierarc...

The shock structure in a binary mixture of polyatomic Eulerian gases with different degrees of freedom of a molecule is studied based on the multi-temperature model of rational extended thermodynamics. Since the system of field equations is hyperbolic, the shock-structure solution is not always regular, and discontinuous parts (sub-shocks) can be f...

The shock structure in a binary mixture of polyatomic Eulerian gases with different degrees of freedom of a molecule is studied based on the multi-temperature model of rational extended thermodynamics. Since the system of field equations is hyperbolic, the shock-structure solution is not always regular, and discontinuous parts (sub-shocks) can be f...

A relativistic version of the Kinetic Theory for polyatomic gas is considered and a new hierarchy of moments that takes into account the total energy composed by the rest energy and the energy of the molecular internal modes is presented. In the first part, we prove via classical limit that the truncated system of moments dictates a precise hierarc...

A relativistic version of the rational extended thermodynamics of polyatomic gases based on a new hierarchy of moments that takes into account the total energy composed by the rest energy and the energy of the molecular internal mode is proposed. The moment equations associated with the Boltzmann–Chernikov equation are derived, and the system for t...

A relativistic version of the rational extended thermodynamics of polyatomic gases based on a new hierarchy of moments that takes into account the total energy composed by the rest energy and the energy of the molecular internal mode is proposed. The moment equations associated with the Boltzmann-Chernikov equation are derived, and the system for t...

We study the emergent dynamics of the continuum thermodynamic Kuramoto model which arises from the continuum limit of the lattice thermodynamic Kuramoto (TK) model [17]. The continuum TK model governs the time-evolution of the Kuramoto phase field in a temperature field, and the solution to the lattice TK model corresponds to the simple function-va...

Motivated by a recent paper of Pennisi in the relativistic framework Pennisi (2021), we revisit the previous approach of two hierarchies of moments critically and propose a new natural physical hierarchy of moments to describe classical rarefied non-polytropic polyatomic gas in the framework of Molecular Rational Extended Thermodynamics. The differ...

Motivated by a recent paper of Pennisi (2021) in the relativistic framework, we revisit the previous approach of two hierarchies of moments critically and propose a new natural physical hierarchy of moments to describe classical rarefied non-polytropic polyatomic gas in the framework of Molecular Rational Extended Thermodynamics. The differential s...

Rational extended thermodynamics (RET) is the theory that is applicable to nonequilibrium phenomena out of local equilibrium. It is expressed by the hyperbolic system of field equations with local constitutive equations and is strictly related to the kinetic theory with the closure method of the hierarchies of moment equations. The book intends to...

In this chapter, we discuss the parabolic limit of RET via the Maxwellian iteration, and we observe that the usual constitutive equations, which are nonlocal in space, are approximations of some balance laws of RET when some relaxation times are very small. An important consequence is that these equations need not satisfy the objectivity principle....

We present in this chapter a relativistic model of a mixture of Euler gases with multi-temperature. We explicitly determine the production terms resulting from the interchange of energy-momentum between the components by using the entropy principle. We use the analogy between the homogeneous case of a mixture of gases and the thermo-mechanical Cuck...

We present a thermodynamically consistent particle (TCP) model motivated by the theory of multi-temperature mixture of fluids in the spatially homogeneous case. The model incorporates the Cucker-Smale (C-S) type flocking model as its isothermal approximation. It is more complex than the C-S model, because the mutual interactions are not only “mecha...

In this chapter, we explain briefly the relativistic RET of a polyatomic gas with many moments associated with the relativistic Boltzmann-Chernikov kinetic equation truncated at the tensorial index N. We consider the classical limit when c →∞, and we find a natural order and new hierarchies for classical moments that are completely fixed for a give...

In this chapter, we study the shock wave structure in a mixture on the basis of the model of multi-temperature (MT) mixtures explained in Chap. 28. For simplicity, the study is restricted to shocks in a binary mixture of ideal gases (component-1 and 2) that have no viscosity and no heat conductivity. In the first part, we focus our attention on sub...

In the present paper, we give the parabolic limit of the field equations of a recent hyperbolic model of relativistic polyatomic gas in the framework of Rational Extended Thermodynamics (RET) theory. We obtain in this way the corresponding constitutive equations of the Thermodynamics of Irreversible Processes (TIP) obtained first in the context of...

We present a survey on the results concerning some different models of mixture of compressible fluids. In particular, we discuss the most realistic case of mixture where each component has its own temperature ( MT). We first compare the solutions of this model to the one with unique common temperature (ST). In the case of Eulerian fluids, it is sho...

System of balance laws of mixture type is a system of partial differential equations that has a structure similar to the system of a mixture of continuous media, i.e., its main part of the operator is composed of the main parts of several components and the interactions among the components are caused only through the production terms (see Definiti...

We list up some open problems, and discuss briefly the perspective on RET.

We consider the thermodynamic Kuramoto model proposed in [27]. For each oscillator in thermodynamic Kuramoto model, there is a coupling effect between the phase and the temperature field. For such a model, we study a uniform stability and uniform-in-time mean-field limit to the corresponding kinetic equation. For this, we first derive a uniform lp-...

In this article, we study some fundamental properties of nonlinear waves and the Riemann problem of Euler’s relativistic system when the constitutive equation for energy is that of Synge for a monatomic rarefied gas or its generalization for diatomic gas. These constitutive equations are the only ones compatible with the relativistic kinetic theory...

The aim of this paper is to construct the molecular extended thermodynamics for classical rarefied polyatomic gases with a new hierarchy, which is absent in the previous procedures of moment equations. The new hierarchy is deduced recently from the classical limit of the relativistic theory of moments associated with the Boltzmann–Chernikov equatio...

Recently, a novel relativistic polyatomic BGK model was suggested by Pennisi and Ruggeri [J. of Phys. Conf. Series, 1035, (2018)] to overcome drawbacks of the Anderson-Witting model and Marle model.In this paper, we prove the unique existence and asymptotic behavior of classical solutions to the relativistic polyatomic BGK model when the initial da...

An investigation on the features of the shock structure solution of the 13-moment system of extended thermodynamics with a second-order closure based on the maximum entropy principle is presented. The results are compared to those obtained by means of the traditional first-order closure and to those obtained in the framework of kinetic theory by so...

A RET theory of dissipative dense gases is presented. In this chapter, we study, in particular, the RET theory with six fields, where we ignore the shear viscosity and heat conductivity and we treat the internal (rotational and vibrational) motion of a molecule as a unit. We postulate a principle of duality between rarefied gas and dense gas. This...

We consider molecular extended thermodynamics (molecular ET) of rarefied polyatomic gases with the system composed of two hierarchies of balance equations for the moments of a distribution function. The internal degrees of freedom of a molecule are properly taken into account in the distribution function. By the reasoning of physical relevance, the...

In this chapter, we make a survey on the mathematical structure of the system of rational extended thermodynamics, which is strictly related to the mathematical problems of hyperbolic systems in balance form with a convex entropy density. We summarize the main results: The proof of the existence of the main field in terms of which a system becomes...

In this chapter, we present the theory of fluctuating hydrodynamics based on the ET14 theory of rarefied polyatomic gases. And we discuss the link between the two levels of description of fluctuating hydrodynamics, that is, the ET14 theory and the Landau and Lifshitz theory of fluctuating hydrodynamics.

In this chapter, firstly, the relativistic Euler model of a gas is presented with the proof that the system is symmetric hyperbolic for general constitutive equations. In the case of rarefied monatomic gas, by using the relativistic Boltzmann-Chernikov equation, appropriate constitutive equations and, in particular, the Synge energy are discussed....

In this chapter, we propose a natural definition of nonequilibrium temperature and chemical potential. The main field, with which the generalized Gibbs equation is expressed in a differential form, is the key quantity in the definition. In the ET6 theory, in particular, the nonequilibrium temperature and chemical potential coincide exactly with tho...

Experiments of light scattering in a gas afford us with precise information about irreversible processes in a gas even out of local equilibrium. These are a good test for checking the validity of a nonequilibrium thermodynamic theory. In this chapter, we study light scattering on the basis of the ET14 theory.

In this chapter, we study shock wave structure in a rarefied polyatomic gas by using the ET14 theory. We show how the ET14 theory can overcome the difficulties encountered in the previous approaches: Bethe–Teller approach and Gilbarg–Paolucci approach. Firstly, the predictions derived from the ET14 theory are shown and compared with the results fro...

As seen in the previous chapters, the role of the dynamic pressure in nonequilibrium phenomena can be highlighted in the ET6 and ET7 theories by ignoring other dissipative processes. These theories are particularly important for gases with the large relaxation time of the dynamic pressure. In this chapter, taking the role into special account, we s...

The objective of the present chapter is to explain the phenomenological RET theory (ET14) of rarefied polyatomic gases with 14 independent fields, that is, mass density, velocity, temperature, shear stress, dynamic pressure, and heat flux. A gas is assumed to be non-polytropic, that is, the internal energy density of a gas has the nonlinear depende...

In this chapter, we prove, in the case of rarefied polyatomic gas with non-polytropic caloric equation of state, that the maximum entropy principle (MEP) gives the same closed system as that obtained in the phenomenological RET theory with 14 fields discussed in Chap. 6. The key idea for the study of polyatomic gases with MEP is to adopt a generali...

In Chap. 8, we have established the ET15 theory of rarefied polyatomic gases where molecular rotational and vibrational modes are taken into account individually. Thereby, compared with the ET14 theory, we have obtained a more refined version with a wider applicability range. And, in Chaps. 12 and 13, we have constructed the nonlinear ET6 theory by...

We verify the K-condition for the nonlinear ET6 model and show, for any gas, the existence of global smooth solutions provided that initial data are sufficiently small. As an example, in the case of polyatomic gas, we study acceleration waves. We evaluate the Bernoulli equation for the amplitude of the wave. If the initial amplitude of an accelerat...

We study stationary heat conduction in a rarefied polyatomic gas at rest confined in a bounded domain in planar or radial (cylindrical and spherical) geometry by using the ET14 theory. We are particularly interested in the effect of the dynamic pressure Π on heat conduction phenomena because such an effect cannot be observed in a monatomic gas.

In this chapter, before going into details, we give an overview of the present book, starting with a short history of nonequilibrium thermodynamics and the upbringing of Rational Extended Thermodynamics (RET) of rarefied monatomic gases. The new version of RET includes the 14-field theory of rarefied polyatomic gases that reduces to the classical N...

Dealing with the rotational mode and the vibration mode separately, we can study also the RET theories with many moments, which include the ET15 theory (Chap. 8) as a special one with 15 moments. In this chapter, we present very briefly the general triple hierarchy with the discussion about the MEP.

Recently, Pennisi and Ruggeri [J Stat Phys 179, 231-246 (2020)] consider the classical limit of the relativistic theory of moments associated with the Boltzmann-Chernikov equation truncated at a tensorial index $N+1$ and they proved that there exists a unique possible choice of the moments in the classical case for a given $N$ both for monatomic an...

In many physical systems one encounters situations where phenomena occur at different scales. An example is the modeling of a rarefied gas at varying Knudsen number (Kn). Large Kn corresponds to a case where the Boltzmann equation is the most appropriate model while, for small Kn, one can obtain the Euler or Navier–Stokes–Fourier system. At interme...

The temporal evolution of Kuramoto oscillators influenced by the temperature field often appears in biological oscillator ensembles. In this paper, we propose a generalized Kuramoto type lattice model on a regular ring lattice with the equal spacing assuming that each oscillator has an internal energy (temperature). Our lattice model is derived fro...

A classical system of conservation laws descriptive of relativistic gasdynamics is examined. In the two-dimensional stationary case, the system is shown to be invariant under a novel multi-parameter class of reciprocal transformations. The class of invariant transformations originally obtained by Bateman in non-relativistic gasdynamics in connectio...

Wave propagation phenomena give us an important mean to check the validation of a nonequilibrium thermodynamics theory. In this chapter, we present a short review on the modern theory of wave propagation for hyperbolic systems. Firstly, we present the theory of linear waves emphasizing the role of the dispersion relation. The high frequency limit i...

The goal of this chapter is to present the relativistic extended thermodynamics (relativistic ET) theory of rarefied polyatomic gases with 14 fields. This is achieved by adopting the closure procedure for the generalized moments of a distribution function that, as in the classical case, depends on an additional continuous variable representing the...

In the previous Chaps. 6 and 7, we have studied RET of rarefied polyatomic gases under the assumption that molecular internal modes can be treated as a whole in terms of the single variable I. However, by dividing the internal modes into the molecular rotational and vibrational modes, we can obtain a more refined version of RET of rarefied polyatom...

We establish extended thermodynamics of rarefied polyatomic gases with six independent fields via the maximum entropy principle. The distribution function is not necessarily near equilibrium. The result is in perfect agreement with the phenomenological RET theory explained in Chap. 12. This is the first example of molecular ET with a nonlinear clos...

In this chapter, we study a RET theory of dense polyatomic gases taking into account the experimental evidence that the relaxation times of molecular rotation and that of molecular vibration are quite different from each other. For simplicity, as in Chap. 24, we focus on the bulk viscosity but ignore the shear viscosity and the heat conductivity. T...

In this chapter, we present a RET theory of rarefied polyatomic gases with 6 independent fields (ET6), i.e., the mass density, the velocity, the temperature, and the dynamic pressure, without adopting the near-equilibrium approximation. This model takes into account the dissipation process in a gas only through the dynamic pressure. By ignoring bot...

In this chapter, we study a linear sound wave in a rarefied polyatomic gas in equilibrium. Thereby we can clarify the validity and the features of the ET14 and ET15 theories established in Chaps. 6–8. In the first half of this chapter, we derive the dispersion relations on the basis of the ET14 theory and of the classical Navier-Stokes and Fourier...

The difference in the theoretical structure between monatomic gas and polyatomic gas in highly nonequilibrium states is discussed from the viewpoint of molecular extended thermodynamics (molecular ET) of rarefied gases, which is free from the local equilibrium assumption. The molecular ET theories of these two types of gas are based on the moment b...

In this chapter, we show the usefulness of both linear and nonlinear ET6 theories for the analysis of shock wave structure in a rarefied polyatomic gas. Firstly we compare the theoretical predictions derived from the linear ET6 theory with those from the ET14 theory. We see, in particular, that the thin layer in Type C with finite thickness describ...

We make a survey about RET of rarefied monatomic gases. In addition to some results that have been already given in the Müller-Ruggeri book (Müller and Ruggeri: Rational Extended Thermodynamics, 2nd edn. Springer, New York (1998)), many others obtained recently are presented. We start from the phenomenological RET theory with 13 fields. We prove th...

The paper aims to construct a rational extended thermodynamics (RET) theory of dense polyatomic gases by taking into account the experimental evidence that the relaxation time of molecular rotation and that of molecular vibration are quite different from each other. For simplicity, we focus on gases with only one dissipative process due to bulk vis...

The balance laws of Rational Extended Thermodynamics describe well the evolution of rarefied gases in non-equilibrium. Usually, it is necessary to approximate the theory in a neighborhood of an equilibrium state and consequently, its hyperbolicity property remains valid only in a neighborhood of the equilibrium state of the field variables, called...

In this paper, we consider a rarefied polyatomic gas with a non-polytropic equation of state. We use the variational procedure of maximum entropy principle (MEP) to obtain the closure of the binary hierarchy of 14 moments associated with the Boltzmann equation in which the distribution function depends also on the energy of internal modes. The clos...

The compatibility between balance laws and the entropy principle implies that any hyperbolic system becomes a Godunov symmetric system if we choose as variables the main field. The consequence is the well-posedness of Cauchy problem. Rational Extended Thermodynamics (RET) is a theory for nonequilibrium gases that belongs in this mathematical framew...

Invariance of a 1+1-dimensional relativistic isentropic gasdynamic system is established under two multi-parameter classes of transformation. The latter constitute, in turn, extensions of reciprocal and Movsesian-type invariance transformations with origin in classical non-relativistic gasdynamics.

The moment system associated with the Boltzmann equation is largely used in many applications and is the main ingredient of Rational Extended Thermodynamics (RET). The choice of truncation of moments is arbitrary and many possibilities are present in the literature depending in particular on many contracted indexes in each moment tensor considered....

Recently, Ruggeri et al. (The Riemann problem of relativistic Euler system with Synge energy, arXiv:2001.04128v1 [math-ph], 2020) studied the Riemann problem of the relativistic Euler system for rarefied monatomic and diatomic gases with a constitutive equation for the energy determined by Synge, which is the only realistic equation compatible with...

The temporal evolution of Kuramoto oscillators influenced by the temperature field often appears in biological oscillator ensembles. In this paper, we propose a generalized Kuramoto type lattice model on a regular ring lattice with the equal spacing assuming that each oscillator has an internal energy (temperature). Our lattice model is derived fro...

We present a relativistic model for a mixture of Euler gases with multiple temperatures. For the proposed relativistic model, we explicitly determine production terms resulting from the interchange of energy–momentum between the constituents via the entropy principle. We use the analogy with the homogeneous solutions of a mixture of gases and the t...

There are three different levels of description for macroscopic physical systems: macroscopic level using thermodynamics and continuum mechanics, mesoscopic level by the kinetic theory, and microscopic level by statistical mechanics of many-particle systems. The search for possible links bridging among these levels is the core part of the Hilbert S...

In this paper, we study the Riemann problem of relativistic Euler system for rarefied monatomic and diatomic gases when the constitutive equation for the energy is the Synge equation that is the only one compatible with the relativistic kinetic theory. The Synge equation is involved with modified Bessel functions of the second kind and this makes t...

The rational extended thermodynamics theory describes non-equilibrium phenomena for rarefied gases, and it is usually approximated in the neighborhood of an equilibrium state. Consequently, the hyperbolicity of its differential system holds only in some domain of the state variables (called hyperbolicity region). In this paper, we present a second-...

We present the state of the art of the mathematical theory of shock waves for hyperbolic systems. We start with a brief review of ideal shock waves discussing, in particular, the Riemann problem and the phase transition induced by shock waves in real gases. Then we consider dissipative systems and summarise the results concerning the behaviour of t...

The spherical shock wave in a rarefied polyatomic gas is analyzed based on Rational Extended Thermodynamics (RET) with six independent fields; the mass density, velocity, pressure and dynamic pressure. By adopting the method on the basis of Lie group theory proposed in [A. Donato and T. Ruggeri, Similarity Solutions and Strong Shocks in Extended Th...

The goal of this paper is to obtain a precise expression for the production tensor in a dissipative hyperbolic relativistic theory of gas with internal structure. For this aim, we use a variant of relativistic BGK model for the Boltzmann–Chernikov kinetic equation. Moreover, we deduce some inequalities for the coefficients requiring the entropy pri...