Ru Wang, Xiaojun Chang
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.
DOI: https://doi.org/10.58997/ejde.2022.51
Show me the PDF file (398 KB), TEX file for this article.
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Ru Wang School of Mathematics and Statistics Northeast Normal University Changchun 130024, Jilin, China email: wangr076@nenu.edu.cn |
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Xiaojun Chang School of Mathematics and Statistics and Center for Mathematics and Interdisciplinary Sciences Northeast Normal University Changchun 130024, Jilin, China email: changxj100@nenu.edu.cn |
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