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.
作者
罗亮
李霞
LUo Liang;LI Xia(School of Mathematical Sciences,SUST,Suzhou 215009,China)
出处
《苏州科技大学学报（自然科学版）》
CAS
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)。
