Existence and blow-up of solutions for finitely degenerate semilinear parabolic equations with singular potentials

Abstract

In this article, we investigate the initial-boundary value problem for a class of finitely degenerate semilinear parabolic equations with singular potential term. By applying the Galerkin method and Banach fixed theorem we establish the local existence and uniqueness of the weak solution. On the other hand, by constructing a family of potential wells, we prove the global existence, the decay estimate and the finite time blow-up of solutions with subcritical or critical initial energy.

Keywords

• finitely degenerate parabolic equation
• singular potentials
• local existence
• potential well
• global existence
• blow-up
• decay estimate