Related papers: Generalized solution to a system of conservation l…
Here we provide uniqueness of vanishing viscosity solutions to sub-Riemannian mean curvature flow problem, which was known only far from characteristic points or under special symmetry condition. We employ vanishing viscosity approach and…
Z^2-periodic entropy solutions of hyperbolic scalar conservation laws and Z^2-periodic viscosity solutions of Hamilton-Jacobi equations are not unique in general. However, uniqueness holds for viscous scalar conservation laws and viscous…
We introduce an adaptive viscosity regularization approach for the numerical solution of systems of nonlinear conservation laws with shock waves. The approach seeks to solve a sequence of regularized problems consisting of the system of…
In this paper, we prove the global existence of general small solutions to compressible viscoelastic system. We remove the "initial state" assumption ($\tilde \rho_0 \det F_0 =1$) and the "div-curl" structure assumption compared with…
We consider a scalar, possibly degenerate parabolic equation with a source term, in several space dimensions. For initial data with bounded variation we prove the existence of solutions to the initial-value problem. Then we show that these…
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…
Method of compensated compactness is used to show that the almost everywhere limit of quasilinear viscous approximations is the unique entropy solution (in the sense of {\it Bardos et.al}\cite{MR542510}) of the corresponding scalar…
The purpose of this work is to investigate the Cauchy problem of global-in-time existence of large strong solutions to the Navier-Stokes equations for compressible viscous and heat conducting fluids. A class of density-dependent viscosity…
Balanced Viscosity solutions to rate-independent systems arise as limits of regularized rate-independent flows by adding a superlinear vanishing-viscosity dissipation. We address the main issue of proving the existence of such limits for…
We are concerned with the global existence of finite-energy entropy solutions of the one-dimensional compressible Euler equations with (possibly) damping, alignment forces, and nonlocal interactions: Newtonian repulsion and quadratic…
In this paper, we consider unsaturated poroelasticity, i.e., coupled hydro-mechanical processes in unsaturated porous media, modeled by a non-linear extension of Biot's quasi-static consolidation model. The coupled, elliptic-parabolic…
We consider a generalization of the compressible barotropic Navier-Stokes equations to the case of non-Newtonian fluid in the whole space. The viscosity tensor is assumed to be coercive with an exponent $q>1.$ We prove that if the total…
Motivated by many applications (geophysical flows, general relativity), we attempt to set the foundations for a study of entropy solutions to nonlinear hyperbolic conservation laws posed on a (Riemannian or Lorentzian) manifold. The flux of…
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…
This paper investigates the Cauchy problem for the barotropic compressible Navier-Stokes equations in $\mathbb{R}^2$ with the constant state as far field, which may be vacuum or non-vacuum. Under the assumption of a sufficiently large bulk…
Some cylindrically symmetric inhomogeneous viscous fluid cosmological models with electro-magnetic field are obtained. To get a solution a supplementary condition between metric potentials is used. The viscosity coefficient of bulk viscous…
In this paper, we discuss the asymptotic behaviour of weak solutions to the Cauchy problem toward the viscous shock waves for the scalar viscous conservation law. We firstly consider the case that the flux function is the quadratic Burgers…
We study global well-posedness of strong solutions for the nonhomogeneous Navier-Stokes equations with density-dependent viscosity and initial density allowing vanish in $\mathbb{R}^2$. Applying a logarithmic interpolation inequality and…
We address the question of global in time existence of solutions to a magnetoviscoelastic system with general initial data. We show that the notion of dissipative solutions allows to prove such an existence in two and three dimensions. This…
In this paper, we prove the existence of global weak solutions for 3D compressible Navier-Stokes equations with degenerate viscosity. The method is based on the Bresch and Desjardins entropy conservation. The main contribution of this paper…