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.
Mots-clés : Dynamic boundary problems, discrete differential games, viscosity solutions
@article{COCV_2020__26_1_A13_0, author = {Hamamuki, Nao and Liu, Qing}, title = {A deterministic game interpretation for fully nonlinear parabolic equations with dynamic boundary conditions}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, publisher = {EDP-Sciences}, volume = {26}, year = {2020}, doi = {10.1051/cocv/2019076}, mrnumber = {4064473}, zbl = {1442.35230}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2019076/} }
TY - JOUR AU - Hamamuki, Nao AU - Liu, Qing TI - A deterministic game interpretation for fully nonlinear parabolic equations with dynamic boundary conditions JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2020 VL - 26 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2019076/ DO - 10.1051/cocv/2019076 LA - en ID - COCV_2020__26_1_A13_0 ER -
%0 Journal Article %A Hamamuki, Nao %A Liu, Qing %T A deterministic game interpretation for fully nonlinear parabolic equations with dynamic boundary conditions %J ESAIM: Control, Optimisation and Calculus of Variations %D 2020 %V 26 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2019076/ %R 10.1051/cocv/2019076 %G en %F COCV_2020__26_1_A13_0
Hamamuki, Nao; Liu, Qing. A deterministic game interpretation for fully nonlinear parabolic equations with dynamic boundary conditions. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 13. doi : 10.1051/cocv/2019076. http://archive.numdam.org/articles/10.1051/cocv/2019076/
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