Related papers: Singular limits in phase dynamics with physical vi…
We prove the uniqueness of solutions to the Dafermos regularization viscous wave fan profiles for Riemann solutions of scalar hyperbolic conservation laws. We emphasize that our results are not restricted to the small self-similar viscosity…
We provide a precise description of the set of residual boundary conditions generated by the self-similar viscous approximation introduced by Dafermos et al. We then apply our results, valid for both conservative and non conservative…
Systems of the first order partial differential equations with singular solutions appear in many multiphysics problems and the weak formulation of solutions involve in many cases product of distributions. In this paper we study such a…
We present counter-intuitive examples of a viscous regularizations of a two-dimensional strictly hyperbolic system of conservation laws. The regularizations are obtained using two different viscosity matrices. While for both of the…
In this paper we consider the hyperbolic-elliptic system of two conservation laws that describes the dynamics of an elastic material governed by a non-monotone strain-stress function. Following Abeyaratne and Knowles, we propose a notion of…
We prove the well--posedness of a dynamical perfect plasticity model under general assumptions on the stress constraint set and on the reference configuration. The problem is studied by combining both calculus of variations and hyperbolic…
We investigate various analytical and numerical techniques for the coupling of nonlinear hyperbolic systems and, in particular, we introduce here an augmented formulation which allows for the modeling of the dynamics of interfaces between…
We study the inflow-outflow boundary value problem on an interval, the analog of the 1D shock tube problem for gas dynamics, for general systems of hyperbolic-parabolic conservation laws. In a first set of investigations, we study…
We consider solutions of two-dimensional $m \times m$ systems hyperbolic conservation laws that are constant in time and along rays starting at the origin. The solutions are assumed to be small $L^\infty$ perturbations of a constant state…
We deal with initial-boundary value problems for systems of conservation laws in one space dimension and we focus on the boundary Riemann problem. It is known that, in general, different viscous approximations provide different limits. In…
We consider initial boundary-value problems for nonlinear systems of conservation laws in one space variable. It is known that in general different viscous mechanisms yield different solutions in the zero-viscosity limit. Here we focus on…
This paper is concerned with the asymptotic stability of the solution to an initial-boundary value problem on the half line for a hyperbolic-elliptic coupled system of the radiating gas, where the data on the boundary and at the far field…
We introduce a notion of viscosity solutions for a general class of elliptic-parabolic phase transition problems. These include the Richards equation, which is a classical model in filtration theory. Existence and uniqueness results are…
In this note we study the singular vanishing-viscosity limit of a gradient flow set in a finite-dimensional Hilbert space and driven by a smooth, but possibly non convex, time-dependent energy functional. We resort to ideas and techniques…
The aim of this paper is to answer the question: Do the controls of a vanishing viscosity approximation of the one dimensional linear wave equation converge to a control of the conservative limit equation? Our viscous term contains the…
In this paper, we establish the well-posedness and large-time asymptotic behavior of viscosity solutions to singular/degenerate parabolic $p$-Laplacian equations with general capillary-type boundary conditions, including Neumann and…
We introduce a new notion of viscosity solutions for a class of very singular nonlinear parabolic problems of non-divergence form in a periodic domain of arbitrary dimension, whose diffusion on flat parts with zero slope is so strong that…
We consider a system of two conservation laws and provide a detailed description of both classical and non-classical self-similar Riemann solutions. In particular, we demonstrate the existence of overcompressive delta shocks as singular…
An exact closure for hydrodynamic variables is rigorously derived from the linear Boltzmann kinetic equation. Our approach, based on spectral theory, structural properties of eigenvectors and the theory of slow manifolds, allows us to…
We study well-posedness and asymptotic dynamics of a coupled system consisting of linearized 3D Navier--Stokes equations in a bounded domain and a classical (nonlinear) full von Karman shallow shell equations that accounts for both…