A billiard-based game interpretation of the Neumann problem for the curve shortening equation. (English) Zbl 1170.35437

Giga, Yoshikazu; Liu, Qing

Adv. Differ. Equ. 14, No. 3-4, 201-240 (2009).

The authors developed a family of discrete games, whose value functions converge to the unique viscisity solution of the Neumann boundary problem of the curve shortening flow equation. It is to be noted that the Neumann boundary value problems of mean curvature flow equations can be intemately connected with purely deterministic game theory.

Reviewer: Prabhat Kumar Mahanti (Ranchi)

MSC:

35K20	Initial-boundary value problems for second-order parabolic equations
49L25	Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
53C44	Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
91A05	2-person games

Keywords:

game interpretation; Neumann problem; curve shortening; semiflow; game theory; family of discrete games; deterministic game theory