Blow up analysis for a porous media equation with nonlinear sink and nonlinear boundary condition
In this paper, we study porous media equation $u_{t}=\Delta u^{m}-u^{p}$ with nonlinear boundary condition $\frac{\partial u}{\partial\nu}=ku^{q}$. We determine some sufficient conditions for the occurrence of finite time blow-up or global existence. Moreover, lower and upper bounds for blow-up time...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2021-02-01
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| 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=8859 |
| _version_ | 1797830503847428096 |
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| author | Ya Tian Ran Xu Yao Qin |
| author_facet | Ya Tian Ran Xu Yao Qin |
| author_sort | Ya Tian |
| collection | DOAJ |
| description | In this paper, we study porous media equation $u_{t}=\Delta u^{m}-u^{p}$ with nonlinear boundary condition $\frac{\partial u}{\partial\nu}=ku^{q}$. We determine some sufficient conditions for the occurrence of finite time blow-up or global existence. Moreover, lower and upper bounds for blow-up time are also derived by using various inequality techniques. |
| first_indexed | 2024-04-09T13:37:11Z |
| format | Article |
| id | doaj.art-4d50ebfdfec847dcb769d3e6f37285c1 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:37:11Z |
| publishDate | 2021-02-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-4d50ebfdfec847dcb769d3e6f37285c12023-05-09T07:53:10ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752021-02-012021811110.14232/ejqtde.2021.1.88859Blow up analysis for a porous media equation with nonlinear sink and nonlinear boundary conditionYa Tian0Ran Xu1Yao Qin2Chongqing University of Posts and Telecommunications, Chongqing, P.R. ChinaChongqing University of Posts and Telecommunications, Chongqing, P.R. ChinaChongqing University of Posts and Telecommunications, Chongqing, P.R. ChinaIn this paper, we study porous media equation $u_{t}=\Delta u^{m}-u^{p}$ with nonlinear boundary condition $\frac{\partial u}{\partial\nu}=ku^{q}$. We determine some sufficient conditions for the occurrence of finite time blow-up or global existence. Moreover, lower and upper bounds for blow-up time are also derived by using various inequality techniques.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=8859porous media equationnonlinear boundary conditionbounds for blow-up time |
| spellingShingle | Ya Tian Ran Xu Yao Qin Blow up analysis for a porous media equation with nonlinear sink and nonlinear boundary condition Electronic Journal of Qualitative Theory of Differential Equations porous media equation nonlinear boundary condition bounds for blow-up time |
| title | Blow up analysis for a porous media equation with nonlinear sink and nonlinear boundary condition |
| title_full | Blow up analysis for a porous media equation with nonlinear sink and nonlinear boundary condition |
| title_fullStr | Blow up analysis for a porous media equation with nonlinear sink and nonlinear boundary condition |
| title_full_unstemmed | Blow up analysis for a porous media equation with nonlinear sink and nonlinear boundary condition |
| title_short | Blow up analysis for a porous media equation with nonlinear sink and nonlinear boundary condition |
| title_sort | blow up analysis for a porous media equation with nonlinear sink and nonlinear boundary condition |
| topic | porous media equation nonlinear boundary condition bounds for blow-up time |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=8859 |
| work_keys_str_mv | AT yatian blowupanalysisforaporousmediaequationwithnonlinearsinkandnonlinearboundarycondition AT ranxu blowupanalysisforaporousmediaequationwithnonlinearsinkandnonlinearboundarycondition AT yaoqin blowupanalysisforaporousmediaequationwithnonlinearsinkandnonlinearboundarycondition |