Extinction behavior of solutions for the [formula omitted]-Laplacian equations with nonlocal sources

Abstract

We investigate the extinction, non-extinction and decay estimates of non-negative nontrivial weak solutions of the initial-boundary value problem for the p-Laplacian equation with nonlocal nonlinear source and interior linear absorption. We show that the critical exponent of extinction for the weak solution is determined by the competition of two nonlinear terms, and decay estimates depend on the choices of initial data, coefficients and domain.