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Solvability of free boundary problems for steady groundwater flow

Published online by Cambridge University Press:  12 May 2015

A. Yu. BELIAEV
A. Yu. BELIAEV*
Affiliation:
Water Problem Institute, Moscow, Russia email: [email protected]
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Abstract

In this paper the free boundary problem for groundwater phreatic surface is represented in the form of a variational principle. It is proved that the flow domain Ω that solves the problem is a minimizer of some functional Λ(Ω). Weak solutions are introduced as minimizers of the lower semi-continuous regularization of Λ(⋅). Within this approach the existence of weak solutions is proved for a wide class of input data.

Keywords

Free boundary problemsFlows in porous mediaVariational methods
Type
Papers
Information
European Journal of Applied Mathematics , Volume 26 , Issue 6 , December 2015 , pp. 821 - 847
Copyright
Copyright © Cambridge University Press 2015 

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