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 |
| Summary: | 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 $$ - abla(| abla psi|^{p-2} abla psi)=lambda |psi|^{p-2}psi,quadhbox{in } Omega;quad psi|_{partialOmega}=0. $$ |
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| ISSN: | 1072-6691 |