Blow-up analysis in a quasilinear parabolic system coupled via nonlinear boundary flux
This paper deals with the blow-up of the solution for a system of evolution $p$-Laplacian equations $u_{it}=\text{div}(|\nabla u_{i}|^{p-2}\nabla u_{i})\;(i=1,2,\dots,k)$ with nonlinear boundary flux. Under certain conditions on the nonlinearities and data, it is shown that blow-up will occur at som...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2021-02-01
|
| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=8749 |
| _version_ | 1797830419340591104 |
|---|---|
| author | Pan Zheng Zhonghua Xu Zhangqin Gao |
| author_facet | Pan Zheng Zhonghua Xu Zhangqin Gao |
| author_sort | Pan Zheng |
| collection | DOAJ |
| description | This paper deals with the blow-up of the solution for a system of evolution $p$-Laplacian equations $u_{it}=\text{div}(|\nabla u_{i}|^{p-2}\nabla u_{i})\;(i=1,2,\dots,k)$ with nonlinear boundary flux. Under certain conditions on the nonlinearities and data, it is shown that blow-up will occur at some finite time. Moreover, when blow-up does occur, we obtain the upper and lower bounds for the blow-up time. This paper generalizes the previous results. |
| first_indexed | 2024-04-09T13:36:55Z |
| format | Article |
| id | doaj.art-14ef379ccac34881a5027a398db283f1 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:36:55Z |
| publishDate | 2021-02-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-14ef379ccac34881a5027a398db283f12023-05-09T07:53:11ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752021-02-0120211311310.14232/ejqtde.2021.1.138749Blow-up analysis in a quasilinear parabolic system coupled via nonlinear boundary fluxPan Zheng0Zhonghua Xu1Zhangqin Gao2College of Science, Chongqing University of Posts and Telecommunications, Chongqing, P.R. China & College of Mathematics and Statistics, Yunnan University, Kunming, P.R. ChinaCollege of Science, Chongqing University of Posts and Telecommunications, Chongqing, P.R. ChinaCollege of Science, Chongqing University of Posts and Telecommunications, Chongqing, P.R. ChinaThis paper deals with the blow-up of the solution for a system of evolution $p$-Laplacian equations $u_{it}=\text{div}(|\nabla u_{i}|^{p-2}\nabla u_{i})\;(i=1,2,\dots,k)$ with nonlinear boundary flux. Under certain conditions on the nonlinearities and data, it is shown that blow-up will occur at some finite time. Moreover, when blow-up does occur, we obtain the upper and lower bounds for the blow-up time. This paper generalizes the previous results.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=8749blow-upquasilinear parabolic systemnonlinear boundary flux |
| spellingShingle | Pan Zheng Zhonghua Xu Zhangqin Gao Blow-up analysis in a quasilinear parabolic system coupled via nonlinear boundary flux Electronic Journal of Qualitative Theory of Differential Equations blow-up quasilinear parabolic system nonlinear boundary flux |
| title | Blow-up analysis in a quasilinear parabolic system coupled via nonlinear boundary flux |
| title_full | Blow-up analysis in a quasilinear parabolic system coupled via nonlinear boundary flux |
| title_fullStr | Blow-up analysis in a quasilinear parabolic system coupled via nonlinear boundary flux |
| title_full_unstemmed | Blow-up analysis in a quasilinear parabolic system coupled via nonlinear boundary flux |
| title_short | Blow-up analysis in a quasilinear parabolic system coupled via nonlinear boundary flux |
| title_sort | blow up analysis in a quasilinear parabolic system coupled via nonlinear boundary flux |
| topic | blow-up quasilinear parabolic system nonlinear boundary flux |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=8749 |
| work_keys_str_mv | AT panzheng blowupanalysisinaquasilinearparabolicsystemcoupledvianonlinearboundaryflux AT zhonghuaxu blowupanalysisinaquasilinearparabolicsystemcoupledvianonlinearboundaryflux AT zhangqingao blowupanalysisinaquasilinearparabolicsystemcoupledvianonlinearboundaryflux |