Emanuela Radici

Emanuela Radici
Friedrich-Alexander-University Erlangen-Nürnberg | FAU · Chair of Analysis (Nonlinear Partial Differential Equations)

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35
Publications
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213
Citations

Publications

Publications (35)
Article
Full-text available
We investigated existence of global weak solutions for a system of chemotaxis-hapotaxis type with nonlinear degenerate diffusion arising in modelling multiple sclerosis disease. The model consists of three equations describing the evolution of macrophages (m), cytokine (c) and apoptotic oligodendrocytes (d) densities. The main novelty in our work i...
Article
Full-text available
We prove the stability of entropy solutions of nonlinear conservation laws with respect to perturbations of the initial datum, the space-time dependent flux and the entropy inequalities. Such a general stability theorem is motivated by the study of problems in which the flux P[u](t, x, u) depends possibly non-locally on the solution itself. For the...
Preprint
We study a deterministic particle scheme to solve a scalar balance equation with nonlocal interaction and nonlinear mobility used to model congested dynamics. The main novelty with respect to "Radici-Stra [SIAM J.Math.Anal 55.3 (2023)]" is the presence of a source term; this causes the solutions to no longer be probability measures, thus requiring...
Preprint
Full-text available
We propose and analyse a new microscopic second order Follow-the-Leader type scheme to describe traffic flows. The main novelty of this model consists in multiplying the second order term by a nonlinear function of the global density, with the intent of considering the attentiveness of the drivers in dependence of the amount of congestion. Such ter...
Article
We study the discretisation of generalised Wasserstein distances with nonlinear mobilities on the real line via suitable discrete metrics on the cone of N ordered particles, a setting which naturally appears in the framework of deterministic particle approximation of partial differential equations. In particular, we provide a Γ-convergence result f...
Article
Full-text available
Let \partial\mathcal{Q} be the boundary of a convex polygon in \mathbb{R}^2 , e_\alpha=(\cos\alpha,\sin\alpha) and e_{\alpha}^{\bot}=(-\sin\alpha,\cos\alpha) a basis of \mathbb{R}^2 for some \alpha\in[0,2\pi) and \varphi:\partial\mathcal{Q}\to\mathbb{R}^2 a continuous, finitely piecewise linear injective map. We construct a finitely piecewise affin...
Article
We consider a class of aggregation–diffusion equations on unbounded one-dimensional domains with Lipschitz nonincreasing mobility function. We show strong [Formula: see text]-convergence of a suitable deterministic particle approximation to weak solutions of a class aggregation–diffusion PDEs (coinciding with the classical ones in the no vacuum reg...
Preprint
Full-text available
The goal of this paper is to derive the so-called five gradients inequality for optimal transport theory for general cost functions on two class of differentiable manifolds: locally compact Lie groups and compact Riemannian manifolds with Ricci curvature bounded from below.
Article
Full-text available
In the present work we deal with the existence of solutions for optimal control problems associated to transport equations. The behaviour of a population of individuals will be influenced by the presence of a population of control agents whose role is to lead the dynamics of the individuals towards a specific goal. The dynamics of the population of...
Preprint
Let $\partial \mathcal{Q}$ be the boundary of a convex polygon in $\mathbb{R}^2$, $e_\alpha = (\cos\alpha, \sin \alpha)$ and $e_{\alpha}^{\bot} = (-\sin\alpha , \cos \alpha)$ be a basis of $\mathbb{R}^2$ for some $\alpha\in[0,2\pi)$ and $\phi:\partial\mathcal{Q} \to\mathbb{R}^2$ be a continuous, finitely piecewise linear injective map. We construct...
Preprint
We present a classification of area-strict limits of planar $BV$ homeomorphisms. This class of mappings allows for cavitations and fractures but fulfil a suitable generalization of the INV condition. As pointed out by J. Ball [4], these features are expected in limit configurations of elastic deformations. In [12], De Philippis and Pratelli introdu...
Preprint
Full-text available
We prove the stability of entropy solutions of nonlinear conservation laws with respect to perturbations of the initial datum, the space-time dependent flux and the entropy inequalities. Such a general stability theorem is motivated by the study of problems in which the flux $P[u](t,x,u)$ depends possibly non-locally on the solution itself. For the...
Preprint
Full-text available
We consider a class of aggregation-diffusion equations on unbounded one dimensional domains with Lipschitz nonincreasing mobility function. We show strong $L^1$-convergence of a suitable deterministic particle approximation to weak solutions of a class aggregation-diffusion PDEs (coinciding with the classical ones in the no vacuum regions) for any...
Preprint
Full-text available
We study the discretization of generalized Wasserstein distances with nonlinear mobilities on the real line via suitable discrete metrics on the cone of N ordered particles, a setting which naturally appears in the framework of deterministic particle approximation of partial differential equations. In particular, we provide a $\Gamma$-convergence r...
Article
We consider a one-dimensional aggregation-diffusion equation, which is the gradient flow in the Wasserstein space of a functional with competing attractive-repulsive interactions. We prove that the fully deterministic particle approximations with piecewise constant densities introduced in [25] starting from general bounded initial densities converg...
Preprint
Full-text available
We develop deterministic particle schemes to solve non-local scalar conservation laws with congestion. We show that the discrete approximations converge to the unique entropy solution with an explicit rate of convergence under more general assumptions that the existing literature: the velocity fields are less regular (in particular the interaction...
Preprint
Full-text available
We present a classification of strict limits of planar BV homeomorphisms. The authors and S. Hencl showed in a previous work \cite{CHKR} that such mappings allow for cavitations and fractures singularities but fulfill a suitable generalization of the INV condition. As pointed out by J. Ball \cite{B}, these features are physically expected by limit...
Article
In the recent paper [2], it was proved that the closure of the planar diffeomorphisms in the Sobolev norm consists of the functions which are non-crossing (NC), i.e., the functions which can be uniformly approximated by continuous one-to-one functions on grids. A deep simplification of this property is to consider curves instead of grids, so consid...
Preprint
We consider an aggregation-diffusion equation, which is the gradient flow in the Wasserstein space of a functional with competing attractive-repulsive interactions. We prove that the fully deterministic particle approximations introduced in \cite{DiFrancesco-Rosini} starting from general bounded initial densities converge to bounded weak solutions...
Article
Full-text available
The fermionic projector state is a distinguished quasi-free state for the algebra of Dirac fields in a globally hyperbolic spacetime. We construct and analyze it in the four-dimensional de Sitter spacetime, both in the closed and in the flat slicing. In the latter case we show that the mass oscillation properties do not hold due to boundary effects...
Preprint
Full-text available
In the recent paper [2], it was proved that the closure of the planar diffeomorphisms in the Sobolev norm consists of the functions which are non-crossing (NC), i.e., the functions which can be uniformly approximated by continuous one-to-one functions on the grids. A deep simplification of this property is to consider curves instead of grids, so co...
Preprint
We propose an ODE-based derivation for a generalized class of opinion formation models either for single and multiple species (followers, leaders, trolls). The approach is purely deterministic and the evolution of the single opinion is determined by the competition between two mechanisms: the opinion diffusion and the compromise process. Such deter...
Preprint
The fermionic projector state is a distinguished quasi-free state for the algebra of Dirac fields in a globally hyperbolic spacetime. We construct and analyze it in the four-dimensional de Sitter spacetime, both in the closed and in the flat slicing. In the latter case we show that the mass oscillation properties do not hold due to boundary effects...
Article
We show that a planar BV homeomorphism can be approximated in the area strict sense, together with its inverse, with smooth or piecewise affine homeomorphisms.
Article
Given a continuous, injective function j defined on the boundary of a planar open set W, we consider the problem of minimizing the total variation among all the BV homeomorphisms on W coinciding with j on the boundary. We find the explicit value of this infimum in the model case when W is a rectangle. We also present two important consequences of t...
Article
We introduce a new class of planar mappings that allows for cavitations and fractures. The class is the set of strict limits of planar BV homeomorphisms. Each mapping from this class has a proper pointwise representative which is a multifunction, we show that it maps disjoint sets to essentially disjoint sets and that they have an inverse as a prop...
Article
We investigate the existence of weak type solutions for a class of aggregation-diffusion PDEs with nonlinear mobility obtained as large particle limit of a suitable nonlocal version of the follow-the-leader scheme, which is interpreted as the discrete Lagrangian approximation of the target continuity equation. We restrict the analysis to nonnegativ...
Preprint
We investigate the existence of weak type solutions for a class of aggregation-diffusion PDEs with nonlinear mobility obtained as large particle limit of a suitable nonlocal version of the follow-the-leader scheme, which is interpreted as the discrete Lagrangian approximation of the target continuity equation. We restrict the analysis to nonnegativ...
Article
Full-text available
We construct a deterministic, Lagrangian many-particle approximation to a class of nonlocal transport PDEs with nonlinear mobility arising in many contexts in biology and social sciences. The approximating particle system is a nonlocal version of the follow-the-leader scheme. We rigorously prove that a suitable discrete piece-wise density reconstru...
Thesis
This Thesis is devoted to the problem of � finding regular approximations of planar homeomorphisms with respect to several suitable distances having important applications in nonlinear elasticity. By regular approximations we intend either di� ffeomorphisms or piecewise a� ne homeomorphisms. Both the results would be interesting in di� fferent cont...
Article
Full-text available
We prove that a planar piecewise affine homeomorphism phi defined on the boundary of the square can be extended to a piecewise affine homeomorphism h of the whole square, in such a way that parallel to h parallel to(W1),(p) is bounded from above by parallel to phi parallel to(W1, p) for every p >= 1.
Preprint
In this paper we deal with the task of uniformly approximating an $L$-biLipschitz curve by means of piecewise linear ones. This is rather simple if one is satisfied to have approximating functions which are $L'$-biLipschitz, for instance this was already done with $L'= 4L$ in [Daneri-Pratelli, Lemma 5.5]. The main result of this paper is to do the...
Article
Full-text available
In this paper we deal with the task of uniformly approximating an L-biLipschitz curve by means of piecewise linear ones. This is rather simple if one is satisfied to have approximating functions which are L′-biLipschitz, for instance this was already done with L′=4L in DP, Lemma 5.5. The main result of this paper is to do the same with L′=L+ε (whic...

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