Journal of East China Normal University(Natural Science) ›› 2022, Vol. 2022 ›› Issue (2): 9-15.doi: 10.3969/j.issn.1000-5641.2022.02.002

• Mathematics • Previous Articles     Next Articles

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

Suting CHEN, Xia LI*()   

  1. School of Mathematical Sciences, Suzhou University of Science and Technology, Suzhou Jiangsu 215009, China
  • Received:2020-10-13 Online:2022-03-25 Published:2022-03-28
  • Contact: Xia LI


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

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