### Impacto

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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Official URL: http://www.sciencedirect.com/science/article/pii/0022039687901252

## 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 |
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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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