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,+λu+H(x,Dxu,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 λ-minimal carves which realize the 1-periodic viscosity solution.
关键词
Hamilton-Jacobi方程/粘性解/时间周期
Key words
Hamilton-Jacobi equations/viscosity solution/period of time
维普
万方数据