Publication Cover
Applicable Analysis
An International Journal
Volume 56, 1995 - Issue 3-4
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Original Articles

Periodic solutions of a quasilinear parabolic boundary value problem arising in unsaturated flow through a porous medium

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Pages 279-301 | Received 28 Dec 1993, Published online: 20 Jan 2011
 

Abstract

We prove the existence and uniqueness of periodic solutions of the equation ut = φ(u)xx + b(u)x with Dirichlet and N~umann boundary periodic data. The equation arises, for instance, in the mathematical modelling of the flow of groundwater in a homogeneous isotropic unsaturated porous medium. Those kinds of boundary data represent different periodic behaviours on the top and bottom of the medium due, for instance, to the seasons in the course of the years. The equation arises in many other contexts. We improve precedent results in the literature limited to the non degenerate case ( φ'(0) > 0) and uniformly bounded convection terms.

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