A moving boundary problem modelling diffusion with nonlinear absorption

Moving Boundary Problems with Nonlinear Diffusion

Nonlinear diffusion problem with dynamical boundary value

A nonlinear degenerate convection-diffusion initial boundary value problem is studied in a bounded domain. A dynamical boundary condition (containing the time derivative of a solution) is prescribed on the one part of the boundary. This models a non-perfect contact on the boundary. Existence and uniqueness of a weak solution in corresponding function spaces is proved using the backward Euler me...

Reaction-diffusion waves with nonlinear boundary conditions

A reaction-diffusion equation with nonlinear boundary condition is considered in a two-dimensional infinite strip. Existence of waves in the bistable case is proved by the Leray-Schauder method. 1. Formulation of the problem. Reaction-diffusion problems with nonlinear boundary conditions arise in various applications. In physiology, such problems describe in particular development of atheroscle...

A Stochastic Moving Boundary Value Problem

We consider a stochastic perturbation of a moving boundary problem proposed by Ludford and Stewart and studied by Caffarelli and Vazquez. We prove existence and uniqueness.

Porous medium equation with absorption and a nonlinear boundary condition

In this paper we study a porous medium equation with a nonlinear absorption term and a nonlinear boundary condition. We prove existence of weak solutions and also we establish some uniqueness and non uniqueness results for certain range of the parameters that appear in the problem. Finally we deal with the existence of global solutions in time or blow-up. We find in which region of parameters t...