An existence theorem for weak solution of a nonlinear dam problem

Abstract

In this paper, 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.

Keywords:

• p-harmonic equation
• porous media
• free boundary problem
• monotone operator

AMS(MOS)::

• 35R35
• 35M05
• 76S05