Abstract

The paper deals with the construction of a multivalued solution of the Cauchy problem for the Hamilton–Jacobi equation with discontinuous Hamiltonian with respect to the phase variable. The constructed multivalued solution is approximated by a sequence of continuous solutions of auxiliary Cauchy problems of the Hamilton–Jacobi equation with Hamiltonian which is Lipschitz with respect to the phase variable. The results of the study are illustrated by an example.

中文翻译：

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Hamilton-Jacobi方程的多值解的逼近

摘要

本文针对具有不连续哈密顿量的汉密尔顿-雅各比方程的柯西问题的多值解的构造问题。所构造的多值解通过汉密尔顿-雅各比方程的辅助柯西问题的连续解序列来近似，其中汉密尔顿-哈科比方程的相位变量为Lipschitz。实例说明了研究结果。