On a certain degenerate parabolic equation associated with the infinity-laplacian

Goro Akagi; Kazumasa Suzuki

doi:10.3934/proc.2007.2007.18

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2007, Volume 2007: 18-27. Doi: 10.3934/proc.2007.2007.18 open access

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On a certain degenerate parabolic equation associated with the infinity-laplacian

Goro Akagi^1, and
Kazumasa Suzuki^2,

1.
Department of Machinery and Control Systems, College of Systems Engineering and Science,, Shibaura Institute of Technology, 307 Fukasaku, Minuma-ku, Saitama-shi, Saitama 337-8570
2.
Daiwa Institute of Research, 15-6 Fuyuki, Koto-ku, Tokyo 135-8460

Received: August 31, 2006

Revised: December 31, 2006

Published: August 2007

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Abstract

The comparison, uniqueness and existence of viscosity solutions to the Cauchy-Dirichlet problem are proved for a degenerate parabolic equation of the form $u_t$ = $\Delta_(\infty)u$, where $\Delta_(\infty)$ denotes the so-called infinity-Laplacian given by $\Delta_(\infty)u$ = $\Sigma^(N)_(i,j=1) u_x_i u_x_j u_(x_i)_x_j$ . Our proof relies on a coercive regularization of the equation, barrier function arguments and the stability of viscosity solutions.

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Mathematics Subject Classification: Primary: 35K55, 35K65; Secondary: 35D05.

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