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On a nonlinear degenerate parabolic equation in infiltration or evaporation through a porous medium

Díaz Díaz, Jesús Ildefonso and Kersner, R. (1987) On a nonlinear degenerate parabolic equation in infiltration or evaporation through a porous medium. Journal of Differential Equations, 69 (3). pp. 368-403. ISSN 0022-0396

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Abstract

The main result of the paper is the uniqueness of nonnegative solutions of the Cauchy problem and of the first and mixed boundary value problems for a class of degenerate parabolic equations which includes the model equation ut=(um)xx+(un)x, where m≥1 and n>0. In particular, n is allowed to be smaller than one. The proof is based on a refined test function argument. The condition that u be nonnegative is crucial, but the restriction to one space variable is not.

Item Type:Article
Uncontrolled Keywords:Dirichlet boundary conditions; initial data; infiltration; evaporation; porous medium; existence of limit solutions; weak solutions; modulus of continuity; uniqueness
Subjects:Sciences > Mathematics > Differential geometry
ID Code:16390
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