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An existence theorem for an unbounded dam with leaky boundary conditions. (English) Zbl 0834.35144

Bandle, C. (ed.) et al., Elliptic and parabolic problems. Proceedings of the 2nd European conference, Pont-à-Mousson, June 1994. Harlow: Longman Scientific & Technical. Pitman Res. Notes Math. Ser. 325, 64-73 (1995).
The paper is concerned with analytical investigations for a special dam problem. The domain \(\Omega\) representing the porous medium is assumed to be an unbounded, locally Lipschitz domain in \(\mathbb{R}^n\), \(n\geq 3\). The boundary of \(\Omega\) is subdivided into an impervous part, a part in contact with air and a part covered by fluid (water). At the last one, instead of usual Dirichlet conditions, a general leaky boundary condition is imposed.
Due to the complicated geometrical situation the authors analyze a direct weak formulation originally introduced by Brezis, Kinderlehrer, Stampacchia and Alt for the usual dam problem in general domains at the end of the seventies. The main result of the present paper is the existence of a solution which is obtained as monotone limit of solutions of auxiliary problems on truncated domains. Furthermore, some special properties of the solution are derived.
For the entire collection see [Zbl 0817.35005].

MSC:

35R35 Free boundary problems for PDEs
76S05 Flows in porous media; filtration; seepage
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