相关论文: Dynamics of dislocation densities in a bounded cha…

We study a strongly coupled system consisting of a parabolic equation and a singular Hamilton-Jacobi equation in one space dimension. This system describes the dynamics of dislocation densities in a material submitted to an exterior applied…

We study a mathematical model describing the dynamics of dislocation densities in crystals. This model is expressed as a one-dimensional system of a parabolic equation and a first order Hamilton-Jacobi equation that are coupled together. We…

A cross-diffusion system describing ion transport through biological membranes or nanopores in a bounded domain with mixed Dirichlet-Neumann boundary conditions is analyzed. The ion concentrations solve strongly coupled diffusion equations…

We study existence and uniqueness of solutions to a class of nonlinear degenerate parabolic equations, in bounded domains. We show that there exists a unique solution which satisfies possibly inhomogeneous Dirichlet boundary conditions. To…

We show the well-posedness for a large class of degenerate parabolic equations with an additional singularity and mixed Dirichlet-Neumann boundary conditions on bounded Lipschitz domains. The proof is based on an $L^1$-contraction result.…

The uniqueness of bounded weak solutions to strongly coupled parabolic equations in a bounded domain with no-flux boundary conditions is shown. The equations include cross-diffusion and drift terms and are coupled selfconsistently to the…

We study uniqueness of solutions to degenerate parabolic problems, posed in bounded domains, where no boundary conditions are imposed. Under suitable assumptions on the operator, uniqueness is obtained for solutions that satisfy an…

This paper is devoted to the study of some nonlinear parabolic equations with discontinuous diffusion intensities. Such problems appear naturally in physical and biological models. Our analysis is based on variational techniques and in…

We investigate systems of degenerate parabolic equations idealizing reactive solute transport in porous media. Taking advantage of the inherent structure of the system that allows to deduce a scalar Generalized Porous Medium Equation for…

We prove the well posedness of a class of non linear and non local mixed hyperbolic-parabolic systems in bounded domains, with Dirichlet boundary conditions. In view of control problems, stability estimates on the dependence of solutions on…

We investigate the Cauchy-Dirichlet problem for linear parabolic equations in divergence form. Under mild assumptions on the source term and the domain, we prove the existence of globally H\"{o}lder continuous solutions. Notably, our…

In this paper, we give the existence and uniqueness of the strong solution of one dimensional linear parabolic equation with mixed boundary conditions. The boundary conditions can be any kind of mixed Dirichlet, Neumann and Robin boundary…

In this article, we study a two-dimensional singularly perturbed parabolic equation of the convection-diffusion type, characterized by discontinuities in the source term and convection coefficient at a specific point in the domain. These…

We study a system of parabolic equations consisting of a double nonlinear parabolic equations of Forchheimer type coupled with a semilinear parabolic equations. The system describes a fluid-like driven system for active-passive pedestrian…

This article focuses on parabolic equations with rough diffusion coefficients which are ill-posed in the classical sense of distributions due to the presence of a singular forcing. Inspired by the philosophy of rough paths and regularity…

We consider a class of doubly nonlinear degenerate hyperbolic-parabolic equations with homogeneous Dirichlet boundary conditions, for which we first establish the existence and uniqueness of entropy solutions. We then turn to the…

Parabolic equations with homogeneous Dirichlet conditions on the boundary are studied in a setting where the solutions are required to have a prescribed change of the profile in fixed time, instead of a Cauchy condition. It is shown that…

We provide very mild sufficient conditions for space-time domains (non-necessarily cylindrical) which ensure that the continuous Dirichlet problem and the H\"older Dirichlet problem are well-posed, for any parabolic operator in divergence…

We propose a system of two coupled parabolic equations that have degenerate diffusion constants depending on the energy-like variable. The dissipation of the velocity-like variable is fed as a source term into the energy equation leading to…

We investigate linear parabolic equations in divergence form with singular coefficients and non-smooth boundary data. When the diffusion, drift, or potential terms, as well as the initial or boundary conditions, are distributions rather…