On the weakly degenerate Allen-Cahn equation

Abstract

In this paper we consider a one-dimensional Allen-Cahn equation with degeneracy in the interior of the domain and Neumann boundary conditions. We allow the diffusivity coefficient vanish at some point of the space domain and we are addressed on the existence of stable non-constant solution.

Keywords

• degenerate problem
• allen-cahn equation
• stable solution
• primary: 35a15
• secondary: 35b35
• 35a01