Communications on Pure and Applied Analysis (CPAA)

An evolution equation involving the normalized $P$-Laplacian

Pages: 361 - 396, Volume 10, Issue 1, January 2011      doi:10.3934/cpaa.2011.10.361

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Kerstin Does - Mathematisches Institut, Universität zu Köln, 50923 Köln, Germany (email)

Abstract: This paper considers an initial-boundary value problem for the evolution equation associated with the normalized $p$-Laplacian. There exists a unique viscosity solution $u,$ which is globally Lipschitz continuous with respect to $t$ and locally with respect to $x.$ Moreover, we study the long time behavior of the viscosity solution $u$ and compute numerical solutions of the problem.

Keywords:  Parabolic quasilinear PDE, p-Laplacian, viscosity solutions, image processing, game theory.
Mathematics Subject Classification:  Primary: 35K92, 35K61, 35K65, 35Q91; Secondary: 65M06.

Received: February 2010;      Revised: May 2010;      Available Online: November 2010.