%A Suting CHEN, Xia LI
%T The viscosity solution of the discounted Hamilton-Jacobi equation in non-compact space
%0 Journal Article
%D 2022
%J Journal of East China Normal University(Natural Science)
%R 10.3969/j.issn.1000-5641.2022.02.002
%P 9-15
%V 2022
%N 2
%U {https://xblk.ecnu.edu.cn/CN/abstract/article_25981.shtml}
%8 2022-03-25
%X The discounted Hamilton-Jacobi equation (H-J equation) is a special form of the contact Hamilton-Jacobi equation; hence, study of the discounted H-J equation is important. In this article, we first study an expression of the viscosity solution $u_{\lambda}(x,t)$ for the discounted H-J equation in non-compact space. Then, we explore the convergence of the viscosity solution $u_{\lambda}(x,t)$ for a specific discounted H-J equation with $\lambda >0$ in non-compact space for the initial value in different cases.