Multi-dimensional stefan problems with dynamic boundary conditions

Abstract

We consider multi-phase Stefan problems for a class of nonlinear parabolic equations with dynamic boundary conditions formulated in bounded domains in R^N, N≥2. Our dynamic boundary condition is described by a non-linear parabolic (pseudo) differential equation for the boundary temperature. The existence and uniqueness for a weak solution as well as the monotone dependence of the solution upon data will be shown. Our approach to this problem is based on the abstract theory of nonlinear evolution equations governed by time-dependent subdifferentials in Hilbert spaces.

Keywords:

• nonlinear degenerate parabolic equations
• dynamic boundary conditions
• subdifferentials