Existence of global solutions and blow-up for p-Laplacian parabolic equations with logarithmic nonlinearity on metric graphs
| dc.contributor.author | Wang, Ru | |
| dc.contributor.author | Chang, Xiaojun | |
| dc.date.accessioned | 2023-04-18T18:12:43Z | |
| dc.date.available | 2023-04-18T18:12:43Z | |
| dc.date.issued | 2022-07-18 | |
| dc.description.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. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 18 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.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. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/16612 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.holder | This work is licensed under a Creative Commons Attribution 4.0 International License. | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2022, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Metric graphs | |
| dc.subject | p-Laplace operator | |
| dc.subject | Logarithmic nonlinearity | |
| dc.subject | Global solution | |
| dc.subject | Blow-up | |
| dc.title | Existence of global solutions and blow-up for p-Laplacian parabolic equations with logarithmic nonlinearity on metric graphs | |
| dc.type | Article |