Related papers: Kinetic equations with Maxwell boundary conditions
In this work we study linear Maxwell equations with time- and space-dependent matrix-valued permittivity and permeability on domains with a perfectly conducting boundary. This leads to an initial boundary value problem for a first order…
We consider Stokes systems with measurable coefficients and Lions-type boundary conditions. We show that, in contrast to the Dirichlet boundary conditions, local boundary mixed-norm $L_{s,q}$-estimates hold for the spatial second-order…
We explore singular second-order boundary value problems with mixed boundary conditions on a general time scale. Using the lower and upper solutions method combined with the Brouwer fixed point theorem we demonstrate the existence of a…
We continue our study on the global solution to the two-dimensional Prandtl's system for unsteady boundary layers in the class considered by Oleinik provided that the pressure is favorable. First, by using a different method from [13], we…
The goal of this paper is to study weak solutions of the Fokker-Planck equation. We first discuss existence and uniqueness of weak solutions in an irregular context, providing a unified treatment of the available literature along with some…
Recent results on the fluid dynamic limits of the Boltzmann equation based on the DiPerna-Lions theory of renormalized solutions are reviewed in this paper, with an emphasis on regimes where the velocity field behaves to leading order like…
Laplace interpolation is a popular approach in image inpainting using partial differential equations. The classic approach considers the Laplace equation with mixed boundary conditions. Recently a more general formulation has been proposed…
We prove an existence result for a class of Dirichlet boundary value problems with discontinuous nonlinearity and involving a Leray-Lions operator. The proof combines monotonicity methods for elliptic problems, variational inequality…
In this paper, we introduce a new class of hemivariational inequalities, called dynamic boundary hemivariational inequalities reflecting the fact that the governing operator is also active on the boundary. In our context, it concerns the…
We study a weakly non-linear Fokker-Planck equation with BGK heat thermostats in a spatially bounded domain with conservative Maxwell boundary conditions, presenting a space-dependent accommodation coefficient and a space-dependent…
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 the stability and global existence of weak solutions to a free boundary problem governing the evolution of polymeric fluids. We construct weak solutions of the two-phase model by performing the asymptotic limit of a…
Boundaries occur naturally in kinetic equations and boundary effects are crucial for dynamics of dilute gases governed by the Boltzmann equation. We develop a mathematical theory to study the time decay and continuity of Boltzmann solutions…
We study linear damped and viscoelastic wave equations evolving on a bounded domain. For both models, we assume that waves are subject to an inhomogeneous Neumann boundary condition on a portion of the domain's boundary. The analysis of…
We prove global existence of weak solutions for a version of one velocity Baer-Nunziato system with dissipation describing a mixture of two non interacting viscous compressible fluids in a piecewise regular Lipschitz domain with general…
We study the nonlinear steady Boltzmann equation in the half space, with phase transition and Dirichlet boundary condition. In particular, we study the regularity of the solution to the half-space problem in the situation that the gas is in…
In this paper, we analyze nonlinear differential equations subject to generalized boundary conditions. More specifically, we provide a framework from which we can provide conditions, which are straightforward to check, for the solvability…
We present a stability result for a wide class doubly nonlinear equations, featuring general maximal monotone operators, and (possibly) nonconvex and nonsmooth energy functionals. The limit analysis resides on the reformulation of the…
In this paper we characterise the global stability, global boundedness and recurrence of solutions of a scalar nonlinear stochastic differential equation. The differential equation is a perturbed version of a globally stable autonomous…
A basic question about regularity of Boltzmann solutions in the presence of physical boundary conditions has been open due to characteristic nature of the boundary as well as the non-local mixing of the collision operator. Consider the…