时间周期折现Hamilton-Jacobi方程粘性解的收敛性
Convergence of the Viscosity Solution of Time-periodic Discounted Hamilton-Jacobi Equation
罗亮 1李霞1
作者信息
- 1. 苏州科技大学数学科学学院,苏州 215009
- 折叠
摘要
折现Hamilton-Jacobi方程作为接触Hamilton-Jacobi方程的一种特殊形式,对其研究具有深刻意义.主要研究Tn上时间周期折现Hamilton-Jacobi方程ut+λu+H(x,Dxu,t)=0粘性解的收敛性.若H是Tonelli型哈密尔顿函数,关于t 1-周期,在一定条件下,该方程有唯一的1-周期粘性解ūλ(x,t),本文验证了当n →∞时,limn →∞ uλ(x,t+n)=ūλ(x,t),其中uλ(x,t+n)是ut+λu+H(x,Dxu,t)=0的粘性解.最后以一个具体的时间周期折现Hamilton-Jacobi方程说明了本文的结论.
Abstract
The discounted Hamilton-Jacobi equation is a special form of the contact Hamilton-Jacobi equation.Hence,the study of the discounted Hamilton-Jacobi equation is more intuitionistic.In this paper,we mainly study the convergence of the viscosity solutions of time-periodic discounted Hamilton-Jacobi equation by variational method.For the evolutionary Hamilton-Jacobi equation ut+λu+H(x,Dxu,t)=0,under the assumptions that H(x,p,t)is a Tonelli Hamiltonian,and H(x,p,t)is 1-period in the variable t.we can get the 1-period solution ūλ(x,t)and the 1-periodic solution is unique under the given conditions.Further more,we prove limn→∞ uλ(x,t+n)=ūλ(x,t),where uλ(x,t+n)is the viscosity solution of ut+λu+H(x,Dxu,t)=0.At last,we explain the conclusion with a specific example of Hamilton-Jacobi equation.
关键词
Hamilton-Jacobi方程/粘性解/时间周期Key words
Hamilton-Jacobi equations/viscosity solution/time periodic引用本文复制引用
出版年
2025
NETL
NSTL
万方数据