A deterministic game interpretation for fully nonlinear parabolic equations with dynamic boundary conditions

Hamamuki, Nao; Liu, Qing

doi:10.1051/cocv/2019076

Hamamuki, Nao ; Liu, Qing

ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 13.

Suite au passage du modèle économique de la revue en S20, le texte intégral des articles des années 2019 et 2020 est accessible uniquement sur le site de l'éditeur et est réservé aux abonnés.

Résumé

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.

MR Zbl

DOI : 10.1051/cocv/2019076

Classification : 35K61, 35J66, 35Q91, 35D40
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://www.numdam.org/articles/10.1051/cocv/2019076/}
}

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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://www.numdam.org/articles/10.1051/cocv/2019076/

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