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Zbl 0761.35048
Filo, Ján
Diffusivity versus absorption through the boundary. (English)
[J] J. Differ. Equations 99, No.2, 281-305 (1992). ISSN 0022-0396

In the rectangle $0<x<1$, $0<t<T$, the equation $(u\sp m)\sb t- u\sb{xx}=0$ is considered with positive given initial $u$ and boundary conditions $u\sb x(0,t)=0$, $u\sb x(1,t)=u(1,t)$. The aim of the article is to extend to the general case $m>0$ the results (of global solvability and blow up in finite time) already known for the heat equation $(m=1)$.
[G.Boillat (Aubiere)]

MSC 2000:: *35K57 Reaction-diffusion equations
35Q35 Other equations arising in fluid mechanics
35K15 Second order parabolic equations, initial value problems
35K20 Second order parabolic equations, boundary value problems

Keywords: generalized heat equation; global solvability; blow-up

Cited in: Zbl 0907.35023 Zbl 0790.35042

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