Journal of East China Normal University(Natural Science) >

2022 , Vol. 2022 >Issue 2: 9 - 15

DOI: https://doi.org/10.3969/j.issn.1000-5641.2022.02.002

Mathematics

The viscosity solution of the discounted Hamilton-Jacobi equation in non-compact space

  • Suting CHEN ,
  • Xia LI
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  • School of Mathematical Sciences, Suzhou University of Science and Technology, Suzhou Jiangsu　215009, China

Received date: 2020-10-13

  Online published: 2022-03-28

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Abstract

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.

Key words： Hamilton-Jacobi equation; contact system; viscosity solution

Cite this article

Suting CHEN , Xia LI . The viscosity solution of the discounted Hamilton-Jacobi equation in non-compact space[J]. Journal of East China Normal University(Natural Science), 2022 , 2022(2) : 9 -15 . DOI: 10.3969/j.issn.1000-5641.2022.02.002

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