# Some blowup results for a nonlinear parabolic equation with a gradient term

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

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 07 Faculty of Science > Institute of Mathematics 510 Mathematics gradient dependent nonlinearity; blow-up English 1989 29 Oct 2009 11:19 05 Apr 2016 13:29 Society for Industrial and Applied Mathematics 0036-1429 Copyright © 1989, Society for Industrial and Applied Mathematics https://doi.org/10.1137/0520060 http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0682.35010http://www.ams.org/mathscinet-getitem?mr=1000727
Permanent URL: https://doi.org/10.5167/uzh-22923

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