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An existence theorem for weak solution of a nonlinear dam problem. (English) Zbl 0663.35099

It is shown that the well known p-harmonic equation in the theory of quasi-conformal mappings also describes some porous medium flows. A weak formulation is made for a free boundary problem with a dam domain. An existence theorem is established for this problem which points the way to a computational approach to the solution.
Reviewer: D.M.Wei

MSC:

35R35 Free boundary problems for PDEs
35M99 Partial differential equations of mixed type and mixed-type systems of partial differential equations
76S05 Flows in porous media; filtration; seepage
35A35 Theoretical approximation in context of PDEs
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References:

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