Extinction behavior for a parabolic p-Laplacian equation with gradient source and singular potential

Abstract

We concern with the extinction behavior of the solution for a parabolic p-Laplacian equation with gradient source and singular potential. By energy estimate approach, Hardy-Littlewood-Sobolev inequality, a series of ordinary differential inequalities, and super-solution and sub-solution methods, we obtain the conditions on the occurrence of the extinction phenomenon of the weak solution.

Keywords

• extinction
• parabolic p-laplacian equation
• gradient source
• singular potential