Existence of global solutions and blow-up for p-Laplacian parabolic equations with logarithmic nonlinearity on metric graphs
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Date
2022-07-18
Authors
Wang, Ru
Chang, Xiaojun
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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.
Description
Keywords
Metric graphs, p-Laplace operator, Logarithmic nonlinearity, Global solution, Blow-up
Citation
Wang, R., & Chang, X. (2022). Existence of global solutions and blow-up for p-Laplacian parabolic equations with logarithmic nonlinearity on metric graphs. <i>Electronic Journal of Differential Equations, 2022</i>(51), pp. 1-18.
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Attribution 4.0 International
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This work is licensed under a Creative Commons Attribution 4.0 International License.