Extinction and Non-Extinction of Solutions to a p-Laplace Equation with a Nonlocal Source and an Absorption Term

Abstract

In this short paper, the authors investigate the extinction and non-extinction of solutions to a fast diffusive p-Laplace equation with a nonlocal source and an absorption term. By applying the super-solution and sub-solution methods, instead of energy estimate methods, they give a classification of the exponents and coefficients for the solutions to vanish in finite time or not, which generalizes some previous results.

Keywords:

• p-Laplace equation
• super-solution and sub-solution
• extinction

AMS Subject Classification:

• 35K59
• 35K67