Abstract
This paper is devoted to deterministic discrete game-theoretic interpretations for fully nonlinear parabolic and elliptic equations with nonlinear dynamic boundary conditions. It is known that the classical Neumann boundary condition for general parabolic or elliptic equations can be generated by including reflections on the boundary to the interior optimal control or game interpretations. We study a dynamic version of such type of boundary problems, generalizing the discrete game-theoretic approach proposed by Kohn-Serfaty (2006, 2010) for Cauchy problems and later developed by Giga-Liu (2009) and Daniel (2013) for Neumann type boundary problems.
Funder
Japan Society for the Promotion of Science
Sumitomo Foundation
Inamori Foundation
Central Research Institute, Fukuoka University
Subject
Computational Mathematics,Control and Optimization,Control and Systems Engineering
Cited by
2 articles.
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