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

Abstract

<abstract><p>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.</p></abstract>