Nonlinear diffusion problem with dynamical boundary value

摘要

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. The existence and uniqueness of a weak solution in corresponding function spaces is proved using the backward Euler method for the time discretization. Error estimates for time-discrete approximations are derived.