# American Institute of Mathematical Sciences

2007, 2007(Special): 18-27. doi: 10.3934/proc.2007.2007.18

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

 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, Japan 2 Daiwa Institute of Research, 15-6 Fuyuki, Koto-ku, Tokyo 135-8460, Japan

Received  September 2006 Revised  January 2007 Published  September 2007

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.
Citation: Goro Akagi, Kazumasa Suzuki. On a certain degenerate parabolic equation associated with the infinity-laplacian. Conference Publications, 2007, 2007 (Special) : 18-27. doi: 10.3934/proc.2007.2007.18
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