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

Pages: 18 - 27, Issue Special, September 2007

 Abstract        Full Text (201.1K)              

Goro Akagi - 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 (email)
Kazumasa Suzuki - Daiwa Institute of Research, 15-6 Fuyuki, Koto-ku, Tokyo 135-8460, Japan (email)

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.

Keywords:  Degenerate parabolic equation, infinity-Laplacian, viscosity solution.
Mathematics Subject Classification:  Primary: 35K55, 35K65; Secondary: 35D05.

Received: September 2006;      Revised: January 2007;      Published: September 2007.