Electronic Journal of Differential Equations, Vol. 2022 (2022), No. 51, pp. 1-18.

Title: Existence of global solutions and blow-up for p-Laplacian parabolic
equations with logarithmic nonlinearity on metric graphs
       
Authors: Ru Wang (Northeast Normal Univ., Changchun, Jilin, China)
         Xiaojun Chang (Northeast Normal Univ., Changchun, Jilin, China)

Abstract:   
 In this article, we study the initial-boundary value problem for a p-Laplacian parabolic
equation with logarithmic nonlinearity on compact metric graphs.
Firstly, we apply the Galerkin approximation technique to obtain the existence of a
unique local solution. Secondly, by using the potential well theory with the Nehari manifold,
we establish the existence of global solutions that decay to zero at infinity for all p>1,
and solutions that blow up at finite time when p>2 and at infinity when 1<p≤2.
Furthermore, we  obtain  decay estimates of the global solutions and lower bound
on the blow-up rate.

Submitted April 10, 2022. Published July 18, 2022.
Math Subject Classifications: 35K92, 35B44, 35B40, 35R02.
Key Words: Metric graphs; p-Laplace operator; logarithmic nonlinearity;
           global solution; blow-up.