Sharp threshold for blow-up and global existence in a semilinear parabolic equation with variable source

Abstract

Abstract This paper deals with a semilinear parabolic equation with variable source under the case that the initial energy is less than the potential well depth. We deduce a sharp threshold for blow-up and global existence of solutions. Furthermore, we conclude that the global solution decays as the time goes to infinity.

Keywords

• semilinear parabolic equations
• variable source
• initial energy
• global existence
• blow-up