A deterministic game interpretation for fully nonlinear parabolic equations with dynamic boundary conditions
A deterministic game interpretation for fully nonlinear parabolic equations with dynamic boundary conditions
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DOI：
10.1051/cocv/2019076
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发表时间：
2019-03
期刊：
影响因子：
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通讯作者：
N. Hamamuki;Qing Liu
中科院分区：
文献类型：
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作者：
N. Hamamuki;Qing Liu
本文研究了具有非线性动态边界条件的完全非线性抛物型和椭圆型方程的确定性离散博弈论解释。众所周知，一般抛物型或椭圆型方程的经典Neumann边界条件可以通过在边界上包含对内部最优控制或博弈解释的反射来产生。我们研究了这类边界问题的一个动态版本，推广了Kohn-Serfaty(2006,2010)提出的柯西问题的离散博弈论方法，以及Giga-Liu(2009)和Daniel(2013)后来发展的Neumann型边界问题的离散博弈论方法。
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.