The Blow-Up Time for Solutions of Nonlinear Heat Equations with Small Diffusion

Consider a nonlinear heat equation $u_t - \varepsilon \Delta u = f(u)$ in a cylinder $\{ x \in \Omega ,t > 0\} $, with , $u$ Vanishing on the lateral boundary and $u = \phi _\varepsilon (x)$ initially $(\phi _\varepsilon \geqq 0)$. Denote by $T_\varepsilon $ the blow-up time for the solution. Asy...

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Bibliographic Details
Published in:SIAM journal on mathematical analysis 1987-05, Vol.18 (3), p.711-721
Main Authors: Friedman, Avner, Lacey, Andrew A.
Format: Article
Language:English
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Summary:Consider a nonlinear heat equation $u_t - \varepsilon \Delta u = f(u)$ in a cylinder $\{ x \in \Omega ,t > 0\} $, with , $u$ Vanishing on the lateral boundary and $u = \phi _\varepsilon (x)$ initially $(\phi _\varepsilon \geqq 0)$. Denote by $T_\varepsilon $ the blow-up time for the solution. Asymptotic estimates are obtained for $T_\varepsilon $ as $\varepsilon \to 0$.
ISSN:0036-1410
1095-7154
DOI:10.1137/0518054