Irena Lasiecka

• Doctor of Philosophy
• Distinguished University Professor at University of Memphis

This paper provides a (rigorous) theoretical framework for the numerical approximation of Riccati-based feedback control problems of hyperbolic-like dynamics over a finite-time horizon, with emphasis on genuine unbounded control action. Both continuous and approximation theories are illustrated by specific canonical hyperbolic-like equations with b...

This paper establishes the Unique Continuation Property (UCP) for a suitably overdetermined Magnetohydrodynamics (MHD) eigenvalue problem, which is equivalent to the Kalman, finite rank, controllability condition for the finite dimensional unstable projection of the linearized dynamic MHD problem. It is the ``ignition key" to obtain uniform stabili...

We present an abstract maximal $L^p$-regularity result up to $T = \infty$ on a Banach space, that is tuned to capture (linear) PDEs of parabolic type, defined on a bounded domain and subject to finite dimensional, boundary controls and boundary sensors, in feedback form. It improves Lasiecka et al. (2021), which covered boundary controls and interi...

The motion of a shell is characterized by a system of two coupled hyperbolic partial differential equations: (i) an elastic wave in the two-dimensional in-plane displacement, and (ii) a plate-like Kirchhoff equation in the scalar normal displacement. A dynamic shallow shell is defined on a two-dimensional bounded, smooth manifold with elastic defor...

We consider the d-dimensional MagnetoHydroDynamics (MHD) system defined on a sufficiently smooth bounded domain, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d = 2,3...

The presentation revolves around stability of regularity issues for semigroups corresponding to Euler-Bernoulli plate with localized structural of Kelvin-Voigt damping. New Gevrey regularity as well as exponential and polynomial stability results are established.

We consider an Euler-Bernoulli plate equation with Kelvin-Voigt damping in a bounded domain. The damping is localized in an appropriate open strict subset ω of the domain Ω. While it is known that the solutions of this model with a full damping ω = Ω generates an analytic semigroup, this property is no longer valid for locally distributed damping....

A prototype model for a Fluid–Structure interaction is considered. We aim to stabilize [enhance stability of] the model by having access only to a portion of the state. Toward this goal we shall construct a compensator-based Luenberger design, with the following two goals: (1) reconstruct the original system asymptotically by tracking partial infor...

A prototype model for a Fluid-Structure interaction is considered. We aim to stabilize [enhance stability] of the model by having access only to a portion of the state. Toward this goal we shall construct a compensator-based Luenberger design, with the following two goals: (1) reconstruct the original system asymptotically- by tracking partial info...

2010 AMS: 74F10, 74K20, 76G25, 35B40, 35G25, 37L15

This work is motivated by experimental studies (NASA Langley Research Center) of nonlinear damping mechanisms present in flight structures. It has been observed that the structures exhibit significant nonlinear damping effects which are functions of the energy of the system. The present work is devoted to the study of long-time dynamics to a class...

We consider a structurally damped Euler-Bernoulli plate equation in a bounded domain. The damping is localized in an appropriate open subset of the domain. The damping coefficient is smooth and satisfies some structural conditions. Using the frequency domain approach combined with interpolation inequalities and multipliers technique, we show that t...

Existence of global attractors for a structural-acoustic system, subject to restricted boundary dissipation, is considered. Dynamics of the acoustic environment is given by a linear 3-D wave equation subject to locally distributed boundary dissipation, while the dynamics on the (flat) structural wall is given by a 2D-Kirchhoff-Boussinesq plate equa...

The strong asymptotic stabilization of 3D hyperbolic dynamics is achieved by a damped 2D elastic structure. The model is a Neumann wave-type equation with low regularity coupling conditions given in terms of a nonlinear von Karman plate. This problem is motivated by the elimination of aeroelastic instability (sustained oscillations of bridges, airf...

We consider the linearized third order SMGTJ equation defined on a sufficiently smooth boundary domain in ℝ3$$ {\mathbb{R}}^3 $$ and subject to either Dirichlet or Neumann rough boundary control. Filling a void in the literature, we present a direct general 3×3$$ 3\times 3 $$ system approach based on the vector state solution {position, velocity, a...

Boundary feedback stabilization of a critical third–order (in time) semilinear Jordan–Moore–Gibson–Thompson (JMGT) is considered. The word critical here refers to the usual case where media–damping effects are non–existent or non–measurable and therefore cannot be relied upon for stabilization purposes. Motivated by modeling aspects in high-intensi...

We study the optimal control problem over an infinite time horizon for the third-order JMGT equation, defined on a 3-d bounded domain Ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \be...

The Moore-Gibson-Thompson [MGT] dynamics is considered. This third order in time evolution arises within the context of acoustic wave propagation with applications in high frequency ultrasound technology. The optimal boundary feedback control is constructed in order to have on-line regulation. The above requires wellposedness of the associated Alge...

A partially hinged, partially free rectangular plate is considered, with the aim of addressing the possible unstable end behaviors of a suspension bridge subject to wind. This leads to a nonlinear plate evolution equation with a nonlocal stretching active in the spanwise direction. The wind-flow in the chordwise direction is modeled through a pisto...

In this paper we present an abstract maximal $L^p$-regularity result up to $T = \infty$, that is tuned to capture (linear) Partial Differential Equations of parabolic type, defined on a bounded domain and subject to finite dimensional, stabilizing, feedback controls acting on (a portion of) the boundary. Illustrations include, beside a more classic...

We consider the d-dimensional Boussinesq system defined on a sufficiently smooth bounded domain, and subject to a pair $\{ v, \boldsymbol{u} \}$ of controls localized on $\{ \widetilde{\Gamma}, \omega \}$. Here, $v$ is a scalar Dirichlet boundary control for the thermal equation, acting on an arbitrary small connected portion $\widetilde{\Gamma}$ o...

We consider the d-dimensional Boussinesq system defined on a sufficiently smooth bounded domain, with homogeneous boundary conditions, and subject to external sources, assumed to cause instability. The initial conditions for both fluid and heat equations are taken of low regularity. We then seek to uniformly stabilize such Boussinesq system in the...

We consider 2- or 3-dimensional incompressible Navier-Stokes equations defined on a bounded domain $\Omega$, with no-slip boundary conditions and subject to an external force, assumed to cause instability. We then seek to uniformly stabilize such N-S system, in the vicinity of an unstable equilibrium solution, in critical $L^q$-based Sobolev and Be...

The Jordan–Moore–Gibson–Thompson (JMGT) equation is a well-established and recently widely studied model for nonlinear acoustics (NLA). It is a third–order (in time) semilinear Partial Differential Equation (PDE) with a distinctive feature of predicting the propagation of ultrasound waves at finite speed. This is due to the heat phenomenon known as...

Boundary feedback stabilization of a critical, nonlinear Jordan--Moore--Gibson--Thompson (JMGT) equation is considered. JMGT arises in modeling of acoustic waves involved in medical/engineering treatments like lithotripsy, thermotherapy, sonochemistry, or any other procedures using High Intensity Focused Ultrasound (HIFU). It is a well-established...

The elimination of aeroelastic instability (resulting in sustained oscillations of bridges, buildings , airfoils) is a central engineering and design issue. Mathematically, this translates to strong asymptotic stabilization of a 3D flow by a 2D elastic structure. The stabilization (convergence to the stationary set) of a aerodynamic wave-plate mode...

We consider the third-order (in time) linear equation known as SMGT-equation, as defined on a multidimensional bounded domain. Part A gives optimal interior and boundary regularity results from L2(0,T;L2(Γ)) – Dirichlet or Neumann boundary terms. Explicit representation formulas are given that can be taken to define the notion of solution in the ca...

We consider a structural-acoustic wall problem in three dimensions, in which the structural wall is modeled by a 2D Kirchhoff-Boussinesq plate and the acoustic medium is subject to boundary damping. For this model we study the existence of a continuous nonlinear semigroup associated with the model in the finite energy space. We show that strong/wea...

The (third order in time) JMGT equation [Jordan (J Acoust Soc Am 124(4):2491–2491, 2008) and Cattaneo (C Sulla conduzione del calore Atti Sem Mat Fis Univ Modena 3:83–101, 1948)] is a nonlinear (quasi-linear) partial differential equation (PDE) model introduced to describe a nonlinear propagation of sound in an acoustic medium. The important featur...

The present paper provides a solution in the affirmative to a recognized open problem in the theory of uniform stabilization of 3-dimensional Navier–Stokes equations in the vicinity of an unstable equilibrium solution, by means of a ‘minimal’ and ‘least’ invasive feedback strategy which consists of a control pair \(\{ v,u \}\) (Lasiecka and Triggia...

The Jordan--Moore--Gibson--Thompson (JMGT) equation is a well-established and recently widely studied model for nonlinear acoustics (NLA). It is a third-order (in time) semilinear Partial Differential Equation (PDE) model with the distinctive feature of predicting the propagation of ultrasound waves at \textit{finite} speed due to heat phenomenon k...

We consider 2- or 3-dimensional incompressible Navier–Stokes equations defined on a bounded domain \(\varOmega \), with no-slip boundary conditions and subject to an external force, assumed to cause instability. We then seek to uniformly stabilize such N–S system, in the vicinity of an unstable equilibrium solution, in critical \(L^q\)-based Sobole...

In this paper we present an abstract maximal L^p-regularity result up to T = \infty, that is tuned to capture (linear) Partial Differential Equations of parabolic type, defined on a bounded domain and subject to finite dimensional, stabilizing, feedback controls acting on (a portion of) the boundary. Illustrations include, beside a more classical b...

We consider the 𝑑-dimensional Boussinesq system defined on a sufficiently smooth bounded domain and subject to a pair { v , u } \{v,\boldsymbol{u}\} of controls localized on { Γ ~ , ω } \{\widetilde{\Gamma},\omega\} . Here, 𝑣 is a scalar Dirichlet boundary control for the thermal equation, acting on an arbitrarily small connected portion Γ ~ \widet...

The Jordan-Moore-Gibson-Thompson (JMGT)\cite{christov_heat_2005,jordan_nonlinear_2008,straughan_heat_2014} equation is a benchmark model describing propagation of nonlinear acoustic waves in heterogeneous fluids at rest. This is a third-order (in time) dynamics that accounts for a finite speed of propagation of heat signals. In this paper, we study...

The Jordan-Moore-Gibson-Thompson (JMGT)\cite{christov_heat_2005,jordan_nonlinear_2008,straughan_heat_2014} equation is a benchmark model describing propagation of nonlinear acoustic waves in heterogeneous fluids at rest. This is a third-order (in time) dynamics which accounts for a finite speed of propagation of heat signals (see \cite{coulouvrat_e...

We consider the Moore-Gibson-Thompson equation with memory of type II $$ \partial_{ttt} u(t) + \alpha \partial_{tt} u(t) + \beta A \partial_t u(t) + \gamma Au(t)-\int_0^t g(t-s) A \partial_t u(s)\d s=0 $$ where $A$ is a strictly positive selfadjoint linear operator (bounded or unbounded) and $\alpha,\beta,\gamma>0$ satisfy the relation $\gamma\leq\...

Moore-Gibson-Thompson (MGT) equations, which describe acoustic waves in a heterogeneous medium, are considered. These are the third order in time evolutions of a predominantly hyperbolic type. MGT models account for a finite speed propagation due to the appearance of thermal relaxation coefficient {\tau} {>} {0} in front of the third order time der...

The present paper provides a solution in the affirmative to a recognized open problem in the theory of uniform stabilization of 3-dimensional Navier-Stokes equations in the vicinity of an unstable equilibrium solution, by means of a `minimal' and `least' invasive feedback strategy which consists of a control pair $\{ v,u \}$ \cite{LT2:2015}. Here $...

Our goal is to minimize the fluid vorticity in the case of an elastic body moving and deforming inside the fluid, using a distributed control. This translates into analyzing an optimal control problem subject to a moving boundary fluid–structure interaction (FSI). The FSI is described by the coupling of Navier–Stokes and wave equations. The control...

A partially hinged, partially free rectangular plate is considered, with the aim to address the possible unstable end behaviors of a suspension bridge subject to wind. This leads to a nonlinear plate evolution equation with a nonlocal stretching active in the span-wise direction. The wind-flow in the chord-wise direction is modeled through a piston...

Moore-Gibson-Thompson (MGT) equations, which describe acoustic waves in a heterogeneous medium, are considered. These are the third order in time evolutions of a predominantly hyperbolic type. MGT models account for a finite speed propagation due to the appearance of thermal relaxation coefficient τ>0 in front of the third order time derivative. Si...

We consider the d-dimensional Boussinesq system defined on a sufficiently smooth bounded domain, with homogeneous boundary conditions, and subject to external sources, assumed to cause instability. The initial conditions for both fluid and heat equations are taken of low regularity. We then seek to uniformly stabilize such Boussinesq system in the...

We consider a quasilinear nonhomogeneous, anisotropic Maxwell system in a bounded smooth domain of \(\mathbb {R}^{3}\) with a strictly positive conductivity subject to the boundary conditions of a perfect conductor. Under appropriate regularity conditions, adopting a classical \(L^{2}\)-Sobolev solution framework, a nonlinear energy barrier estimat...

We consider the Moore-Gibson-Thompson equation with memory of type II $$ \partial_{ttt} u(t) + \alpha \partial_{tt} u(t) + \beta A \partial_t u(t) + \gamma Au(t)-\int_0^t g(t-s) A \partial_t u(s){\rm d} s=0 $$ where $A$ is a strictly positive selfadjoint linear operator (bounded or unbounded) and $\alpha,\beta,\gamma>0$ satisfy the relation $\gamma...

We consider an initial–boundary-value problem for a thermoelastic Kirchhoff & Love plate, thermally insulated and simply supported on the boundary, incorporating rotational inertia and a quasilinear hypoelastic response, while the heat effects are modeled using the hyperbolic Maxwell–Cattaneo–Vernotte law giving rise to a ‘second sound’ effect. We...

Fluid structure interaction comprising of an elastic body immersed in the moving fluid is considered. The fluid is modeled by an incompressible Navier-Stokes equations with mixed Dirichlet-Neumann boundary conditions. The goal is to reduce a drag of the obstacle by changing the flow profile on the inlet. This leads to a boundary control problem wit...

We consider a coupled system of a linearly elastic body immersed in a flowing fluid which is modeled by means of the incompressible Navier–Stokes equations with mixed Dirichlet–Neumann-type boundary conditions. For this system we formulate an optimal control problem which amounts to a minimization under constraints of a hydro-elastic pressure at th...

Nonlinear shallow shell models with thermal effects are considered. Such models provide basic prototypes for elastic bodies appearing in the flow/fluid structure interactions. It is assumed that shells are thin and do not account for the regularizing effects of rotary inertia. The nonlinear effects in the model become supercritical, and this raises...

We consider an initial-boundary-value problem for a thermoelastic Kirchhoff & Love plate, thermally insulated and simply supported on the boundary, incorporating rotational inertia and a quasilinear hypoelastic response, while the heat effects are modeled using the hyperbolic Maxwell-Cattaneo-Vernotte law giving rise to a 'second sound' effect. We...

We consider a quasilinear nonhomogeneous, anisotropic Maxwell system in a bounded smooth domain of $\mathbb{R}^{3}$ with a strictly positive conductivity subject to the boundary conditions of a perfect conductor. Under appropriate regularity conditions, adopting a classical $L^{2}$-Sobolev solution framework, a nonlinear energy barrier estimate is...

In these notes, the notion of a strongly continuous semigroup St in a Hilbert space H will be utilized [111, 121, 133]. Frequently, semigroup techniques will be utilized in well-posedness arguments. In most cases below, we eschew arguments based on discretized problems (e.g., using the Galerkin method) in favor of appropriately posing infinite dime...

This paper is concerned with long-time dynamics of a full von Karman system subject to nonlinear thermal coupling and free boundary conditions. In contrast with scalar von Karman system, vectorial full von Karman system accounts for both vertical and in plane displacements. The corresponding PDE is of critical interest in flow structure interaction...

Classical models for the propagation of ultrasound waves are the Westervelt equation, the Kuznetsov and the Khokhlov-Zabolotskaya-Kuznetsov equations. The Jordan-Moore-Gibson-Thompson equation is a prominent example of a Partial Differential Equation (PDE) model which describes the acoustic velocity potential in ultrasound wave propagation, where t...

Classical models for the propagation of ultrasound waves are the Westervelt equation, the Kuznetsov and the Khokhlov-Zabolotskaya-Kuznetsov equations. The Jordan-Moore-Gibson-Thompson equation is a prominent example of a Partial Differential Equation (PDE) model which describes the acoustic velocity potential in ultrasound wave propagation, where t...

The book was inadvertently published with an incorrect author affiliation for Justin T. Webster “University of Maryland, College Park, Maryland, MD, USA” where as it should be “University of Maryland Baltimore County, Baltimore, MD, USA”.

This book is devoted to the study of coupled partial differential equation models, which describe complex dynamical systems occurring in modern scientific applications such as fluid/flow-structure interactions. The first chapter provides a general description of a fluid-structure interaction, which is formulated within a realistic framework, where...

An appearance of utter in oscillating structures is an endemic phenomenon. Most common causes are vibrations induced by the moving flow of a gas which is interacting with the structure. Typical examples include: turbulent jets, vibrating bridges, oscillating facial palate in the onset of apnea.

A third-order in time nonlinear equation with memory term is considered. This particular model is motivated by high-frequency ultrasound technology which accounts for thermal and molecular relaxation. The resulting equations give rise to a quasilinear-like evolution with a potentially degenerate damping (Kaltenbacher in Evol Eqs Control Theory 4(4)...

We address the system of partial differential equations modeling motion of an elastic body inside an incompressible fluid. The fluid is modeled by the incompressible Navier–Stokes equations while the structure is represented by the damped wave equation with interior damping. The additional boundary stabilization γ, considered in our previous paper,...

We study an infinite dimensional finite horizon stochastic linear quadratic control problem in an abstract setting. We assume that the dynamics of the problem are generated by a strongly continuous semigroup, while the control operator is unbounded and the multiplicative noise operators for the state and the control are bounded. We prove an optimal...

Erratum to: V. Barbu et al. (Eds.) Analysis and Optimization of Differential Systems DOI: 10.1007/978-0-387-35690-7

We study an initial-boundary-value problem for a quasilinear thermoelastic plate of Kirchhoff \& Love-type with parabolic heat conduction due to Fourier, mechanically simply supported and held at the reference temperature on the boundary. For this problem, we show the short-time existence and uniqueness of classical solutions under appropriate regu...

We study an initial-boundary-value problem for a quasilinear thermoelastic plate of Kirchhoff \& Love-type with parabolic heat conduction due to Fourier, mechanically simply supported and held at the reference temperature on the boundary. For this problem, we show the short-time existence and uniqueness of classical solutions under appropriate regu...

A third order in time nonlinear equation is considered. This par-ticular model is motivated by High Frequency Ultra Sound (HFU) technology which accounts for thermal and molecular relaxation. The resulting equations give rise to a quasilinear-like evolution with a potentially degenerate damping [23]. The purpose of this paper is twofold: (1) to pro...

We consider a nonlinear (Berger or Von Karman) clamped plate model with a {\em piston-theoretic} right hand side---which include non-dissipative, non-conservative lower order terms. The model arises in aeroelasticity when a panel is immersed in a high velocity linear potential flow; in this case the effect of the flow can be captured by a dynamic p...

We consider a nonlinear (Berger or Von Karman) clamped plate model with a {\em piston-theoretic} right hand side---which include non-dissipative, non-conservative lower order terms. The model arises in aeroelasticity when a panel is immersed in a high velocity linear potential flow; in this case the effect of the flow can be captured by a dynamic p...

We consider a heat-structure interaction model where the structure is subject to viscoelastic (strong) damping. This is a preliminary step toward the study of a fluid-structure interaction model where the heat equation is replaced by the linear version of the Navier-Stokes equation as it arises in applications. We prove four main results: analytici...

We consider a heat–structure interaction model where the structure is subject to viscoelastic (strong) damping. This is a preliminary step toward the study of a fluid–structure interaction model where the heat equation is replaced by the linear version of the Navier–Stokes equation as it arises in applications. We prove four main results: analytici...

We give a survey of recent results on flow-structure interactions modeled by a modified wave equation coupled at an interface with equations of nonlinear elasticity. Both subsonic and supersonic flow velocities are considered. The focus of the discussion here is on the interesting mathematical aspects of physical phenomena occurring in aeroelastici...

We consider the following abstract version of the Moore-Gibson-Thompson equation with memory $$ \partial_{ttt} u(t) + \alpha \partial_{tt} u(t) + \beta A \partial_t u(t) + \gamma Au(t) -\int_0^t g(s) A u(t-s)\d s=0 $$ depending on the parameters $\alpha,\beta,\gamma>0$, where $A$ is strictly positive selfadjoint linear operator and $g$ is a convex...

Asymptotic-in-time interior feedback control of a panel interacting with an inviscid, subsonic flow is considered. The classical model [8] is given by a clamped nonlinear plate strongly coupled to a convected wave equation on the half space. In the absence of energy dissipation the plate dynamics converge to a compact and finite dimensional set [6,...

A. V. Balakrishnan, a co-founder and first, long-time Editor-in-Chief of Applied Mathematics and Optimization, passed away in Los Angeles on March 17, 2015. The scientific community, and in particular our journal’s community, is deeply saddened and mourns his departure. The present special issue of AMO intends to commemorate and cherish his memory...

We consider the long-time behavior of a nonlinear PDE with a memory term which can be recast in the abstract form ddtρ(ut)+Autt+γAθut+Au-∫0tg(s)Au(t-s)=0, where A is a self-adjoint, positive definite operator acting on a Hilbert space H, ρ(s) is a continuous, monotone increasing function, and the relaxation kernel g(s) is a continuous, decreasing f...

We are interested in the Moore–Gibson–Thompson equation with memory $$\tau{u}_{ttt}+ \alpha u_{tt}+c^{2}\mathcal{A}u+b\mathcal{A}u_t -\int_0^{t}g(t-s)\mathcal{A} w(s){\rm {d}}s=0.$$This model arises in high-frequency ultrasound applications accounting for thermal flux and molecular relaxation times. According to revisited extended irreversible ther...

Long time behavior of a third order (in time) nonlinear PDE equation is considered. This type of equations arises in the context of nonlinear acoustics [12,20,22,24] where modeling accounts for a finite speed of propagation paradox, the latter results in hyperbolic nature of the dynamics. It will be proved that the underlying PDE generates a well-p...

In this paper, we consider a simplified version of a fluid-structure PDE model which has been of longstanding interest within the mathematical and biological sciences. In it, a n-dimensional heat equation replaces the original Stokes system, so as to ultimately have a vector-valued heat equation and vector-valued wave equation compose the coupled P...

In this paper, the Shrödinger equation with a defocusing nonlinear term and dynamic boundary conditions defined on a smooth boundary of a bounded domain Ω ⊂ ℝN, N = 2, 3 is considered. Local well-posedness of strong H² solutions is also established. In the case, N = 2 local solutions are shown to be global, and existence of weak H¹ solutions in dim...

A variety of models describing the interaction between flows and oscillating structures are discussed. The main aim is to analyze conditions under which structural instability (flutter) induced by a fluid flow can be suppressed or eliminated. The analysis provided focuses on effects brought about by: (i) different plate and fluid boundary condition...

We consider an unstable Oseen equation (linearized Navier-Stokes equations) defined on a 2-d or 3-d open connected bounded domain and subject to two types of ‘tangential’ controls: (i) a (Dirichlet-type) tangential boundary control acting on an arbitrarily small open sub-portion \(\tilde{\varGamma }\) of positive measure of the full boundary \(\var...

We give a survey of recent results on flow-structure interactions modeled by a modified wave equation coupled at an interface with equations of nonlinear elasticity. Both subsonic and supersonic flow velocities are considered. The focus of the discussion here is on the interesting mathematical aspects of physical phenomena occurring in aeroelastici...

Asymptotic-in-time feedback control of a panel interacting with an inviscid, subsonic flow is considered. The classical model [22] is given by a clamped nonlinear plate strongly coupled to a convected wave equation on the half space. In the absence of imposed energy dissipation the plate dynamics converge to a compact and finite dimensional set [16...

We study a temporally third order (Moore-Gibson-Thompson) equation with a memory term. Previously it is known that, in non-critical regime, the global solutions exist and the energy functionals decay to zero. More precisely, it is known that the energy has exponential decay if the memory kernel decays exponentially. The current work is a generaliza...

A nonlinear model described by von Karman equations with long memory is considered. Hadamard wellposedness of weak solutions, regularity of solutions and intrinsic decay rate estimates for the energy are established by assuming that the memory kernel satisfies the inequality introduced in Alabau-Boussouira and Cannarsa (2009): , where is a given co...