Strong solutions to the Richards equation in the unsaturated zone |
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| Authors: | W Merz |
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| Institution: | a University of Erlangen-Nurnberg, Department of Applied Mathematics I, Martensstr. 3, 91058 Erlangen, Germany
b The University of Warsaw, Institute of Applied Mathematics and Mechanics, Banacha 2, 02-097 Warsaw, Poland |
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| Abstract: | We study the unsaturated case of the Richards equation in three space dimensions with Dirichlet boundary data. We first establish an a priori L∞-estimate. With its help, by means of a fixed point argument we prove global in time existence of a unique weak solution in Sobolev spaces. Finally, we are able to improve the regularity of this weak solution in order to gain a strong one. |
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| Keywords: | Degenerate parabolic equations A priori estimates Strong solutions |
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