Blow-up for p-Laplacian parabolic equations
In this article we give a complete picture of the blow-up criteria for weak solutions of the Dirichlet problem $$ u_t= abla(| abla u|^{p-2} abla u)+lambda |u|^{q-2}u,quad hbox{in } Omega_T, $$ where $p>1$. In particular, for $p>2$, $q=p$ is the blow-up critical exponent and we show that the sh...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2003-02-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2003/20/abstr.html |
| _version_ | 1819039064360222720 |
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| author | Yuxiang Li Chunhong Xie |
| author_facet | Yuxiang Li Chunhong Xie |
| author_sort | Yuxiang Li |
| collection | DOAJ |
| description | In this article we give a complete picture of the blow-up criteria for weak solutions of the Dirichlet problem $$ u_t= abla(| abla u|^{p-2} abla u)+lambda |u|^{q-2}u,quad hbox{in } Omega_T, $$ where $p>1$. In particular, for $p>2$, $q=p$ is the blow-up critical exponent and we show that the sharp blow-up condition involves the first eigenvalue of the problem $$ - abla(| abla psi|^{p-2} abla psi)=lambda |psi|^{p-2}psi,quadhbox{in } Omega;quad psi|_{partialOmega}=0. $$ |
| first_indexed | 2024-12-21T08:47:16Z |
| format | Article |
| id | doaj.art-3b04a6eb007743bebc8f2b6266b34177 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-21T08:47:16Z |
| publishDate | 2003-02-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-3b04a6eb007743bebc8f2b6266b341772022-12-21T19:09:48ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912003-02-01200320112Blow-up for p-Laplacian parabolic equationsYuxiang LiChunhong XieIn this article we give a complete picture of the blow-up criteria for weak solutions of the Dirichlet problem $$ u_t= abla(| abla u|^{p-2} abla u)+lambda |u|^{q-2}u,quad hbox{in } Omega_T, $$ where $p>1$. In particular, for $p>2$, $q=p$ is the blow-up critical exponent and we show that the sharp blow-up condition involves the first eigenvalue of the problem $$ - abla(| abla psi|^{p-2} abla psi)=lambda |psi|^{p-2}psi,quadhbox{in } Omega;quad psi|_{partialOmega}=0. $$http://ejde.math.txstate.edu/Volumes/2003/20/abstr.htmlp-Laplacian parabolic equationsblow-upglobal existencefirst eigenvalue. |
| spellingShingle | Yuxiang Li Chunhong Xie Blow-up for p-Laplacian parabolic equations Electronic Journal of Differential Equations p-Laplacian parabolic equations blow-up global existence first eigenvalue. |
| title | Blow-up for p-Laplacian parabolic equations |
| title_full | Blow-up for p-Laplacian parabolic equations |
| title_fullStr | Blow-up for p-Laplacian parabolic equations |
| title_full_unstemmed | Blow-up for p-Laplacian parabolic equations |
| title_short | Blow-up for p-Laplacian parabolic equations |
| title_sort | blow up for p laplacian parabolic equations |
| topic | p-Laplacian parabolic equations blow-up global existence first eigenvalue. |
| url | http://ejde.math.txstate.edu/Volumes/2003/20/abstr.html |
| work_keys_str_mv | AT yuxiangli blowupforplaplacianparabolicequations AT chunhongxie blowupforplaplacianparabolicequations |