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arXiv · 1806.05851

On the existence, uniqueness and stability of $β$-viscosity solutions to a class of Hamilton-Jacobi equations in Banach spaces

Bang Tran Van·Tien Phan Trong
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Abstract

This paper is concerned with the qualitative properties of viscocity solutions to a class of Hamilton-Jacobi equations (HJEs) in Banach spaces. Specifically, based on the concept of $β$-derivative \cite{DGZ93b} we establish the existence, uniqueness and stability of $β$-viscosity solutions for a class of HJEs in the form $u+H(x,u,Du)=0.$ The obtained results in this paper extend ealier works in the literature, for example, \cite{CL85}, \cite{CL86} and \cite{DGZ93b}.

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Bang Tran Van, Tien Phan Trong. 2018-06-15. On the existence, uniqueness and stability of $β$-viscosity solutions to a class of Hamilton-Jacobi equations in Banach spaces. https://arxiv.org/abs/1806.05851

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