Existence of global solutions and blow-up for p-Laplacian parabolic equations with logarithmic nonlinearity on metric graphs

Electronic Journal of Differential Equations

article

Ru Wang¹  Xiaojun Chang² 

[1] School of Mathematics and Statistics Northeast Normal University Changchun 130024;School of Mathematics and Statistics and Center for Mathematics and Interdisciplinary Sciences Northeast Normal University Changchun 130024

关键词: Metric graphs;    p-Laplace operator;    logarithmic nonlinearity;    global solution;    blow-up.;   

DOI  :  10.58997/ejde.2022.51

学科分类：数学（综合）

来源: Texas State University

【 摘 要 】

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

【 授权许可】

CC BY