Under some conditions, a blowup result is proved for the solution $u$ of: \[\begin{gathered} u_t = \Delta u - \left| {\nabla u} \right|^q + \left| {u} \right|^{p - 1} u,\quad t > 0,\quad x \in \Omega \hfill \\ u(t,x) = 0,\quad t > 0,\quad x \in \Gamma , \hfill \\ u(0,x) = \varphi (x),\quad x \in \Omega . \hfill \\ \end{gathered} \] The associated elliptic problem is also studied. ©1989 Society for Industrial and Applied Mathematics

Chipot, M; Weissler, F (1989). *Some blowup results for a nonlinear parabolic equation with a gradient term.* SIAM Journal on Numerical Analysis, 20(4):886-907.

## Abstract

Under some conditions, a blowup result is proved for the solution $u$ of: \[\begin{gathered} u_t = \Delta u - \left| {\nabla u} \right|^q + \left| {u} \right|^{p - 1} u,\quad t > 0,\quad x \in \Omega \hfill \\ u(t,x) = 0,\quad t > 0,\quad x \in \Gamma , \hfill \\ u(0,x) = \varphi (x),\quad x \in \Omega . \hfill \\ \end{gathered} \] The associated elliptic problem is also studied. ©1989 Society for Industrial and Applied Mathematics

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## Additional indexing

Item Type: | Journal Article, refereed, original work |
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Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |

Dewey Decimal Classification: | 510 Mathematics |

Uncontrolled Keywords: | gradient dependent nonlinearity; blow-up |

Language: | English |

Date: | 1989 |

Deposited On: | 29 Oct 2009 11:19 |

Last Modified: | 05 Apr 2016 13:29 |

Publisher: | Society for Industrial and Applied Mathematics |

ISSN: | 0036-1429 |

Additional Information: | Copyright © 1989, Society for Industrial and Applied Mathematics |

Publisher DOI: | https://doi.org/10.1137/0520060 |

Related URLs: | http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0682.35010 http://www.ams.org/mathscinet-getitem?mr=1000727 |

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