Decay estimate and non-extinction of solutions of p-Laplacian nonlocal heat equations

Abstract

The main goal of this work is to study the initial boundary value problem of a nonlocal heat equations with logarithmic nonlinearity in a bounded domain. By using the logarithmic Sobolev inequality and potential wells method, we obtain the decay, blow-up and non-extinction of solutions under some conditions, and the results extend the results of a recent paper Lijun Yan and Zuodong Yang (2018).

Keywords

• global existence
• decay estimates
• potential well
• blow-up
• non-extinction
• nonlocal heat equations