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Convective Porous Medium Equations with Nonlinear Forcing at the Boundary

✍ Scribed by Mingxin Wang; Shouxin Chen

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 257 KB
Volume: 211
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.1997.5396

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✦ Synopsis

This article deals with the global solutions and blow-up problems for the Ž m . Ž .Ž n . Ž . convective porous medium equation u s u q rn u , x g 0, 1 , t ) 0,

Ž m . Ž . p Ž . Ž m . Ž . with the nonlinear boundary conditions y u 0, t s au 0, t , u 1, t s 0,

w x and positive initial data u x, 0 s u x )0, x g 0, 1 . Here, m, n, , a, and p 0 are all positive constants. Necessary and sufficient conditions for the global existence of all positive solutions are obtained.

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