Dept. Math, Hokkaido Univ. EPrints Server

A Billiard-Based Game Interpretation of the Neumann Problem for the Curve Shortening Equation

Preprint Series # 922
Giga, Yoshikazu and Liu, Qing A Billiard-Based Game Interpretation of the Neumann Problem for the Curve Shortening Equation. (2008);

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Abstract

This paper constructs a family of discrete games, whose value functions converge to the unique viscosity solution of the Neumann boundary problem of the curve shortening flow equation. To derive the boundary condition, a billiard semiflow is introduced and its basic properties near the boundary are studied for convex and more general domains. It turns out that Neumann boundary problems of mean curvature flow equations can be intimately connected with purely deterministic game theory.

Item Type:Preprint
Subjects:35-xx PARTIAL DIFFERENTIAL EQUATIONS
ID Code:1901