An evolution equation involving the normalized $P$-Laplacian
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.
Received: February 2010; Revised: May 2010; Available Online: November 2010.
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