时间周期折现Hamilton-Jacobi方程的粘性解及其性质  

The viscosity solutions of time-periodic discounted Hamilton-Jacobi equations and their properties

作　　者：罗亮 李霞 LUo Liang;LI Xia(School of Mathematical Sciences,SUST,Suzhou 215009,China)

机构地区：[1]苏州科技大学数学科学学院,江苏苏州215009

出　　处：《苏州科技大学学报（自然科学版）》2024年第3期20-27,共8页Journal of Suzhou University of Science and Technology（Natural Science Edition）

基　　金：国家自然科学基金项目(11971344)。

摘　　要：主要研究紧空间上时间周期折现Hamilton-Jacobi方程u_(t)+λu+H(x,D_(x)u,t)=0粘性解的表达形式及其动力系统性质。若H是Tonelli型Hamilton函数,将给出该方程在初值一定时粘性解的表达式,进一步地,给出其1-周期解的表达式,在所给条件下,该周期解是其唯一的1-周期粘性解,并给出了实现1-周期粘性解的λ-极小曲线的一致有界性。In this paper,we mainly studied the expressions of the viscosity solutions of time-periodic discounted Hamilton-Jacobi equations and their dynamical properties.For the equation u_(t)+λu+H(x,D_(x)u,t)=0 we gave the expression of the viscosity solution with a given initial function first under the assumption that H(x,p,t)is a Tonelli Hamilton function.Furthermore,the expression of the 1-periodic solution of the equation was given and the 1-periodic solution was the unique solution of the equation under the given conditions.Finally,we proved the uniform boundedness of the-minimal carves which realize the 1-periodic viscosity solution.

关 键 词：HAMILTON-JACOBI方程 粘性解 时间周期 

分 类 号：O193[理学—数学]