On Approximation of Multivalued Solution for Hamilton-Jacobi equation

被引：0

作者：

Kolpakova, Ekaterina A. ^{[1
]}

机构：

[1] Ural Fed Univ, Krasovskii Inst Math & Mech UrB RAS, Ekaterinburg, Russia

来源：

IFAC PAPERSONLINE | 2018年 / 51卷 / 32期

关键词：

Hamilton-Jacobi equation; multivalued solution; minimax/viscosity solution; convergence in L-1; viability set; VISCOSITY SOLUTIONS;

D O I：

10.1016/j.ifacol.2018.11.447

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

The paper deals with the Cauchy problem for Hamilton Jacobi equation with discontinuous w.r.t. state variable Hamiltonian. In this case we use the notion of M-solution proposed by Subbotin. We consider the sequence of auxiliary Cauchy problems for Hamilton Jacobi equations with Lipschitz continuous w.r.t. phase variable Hamiltonians. We show that the sequence of distances between of graphs of solutions for auxiliary Cauchy problems and graph of M-solution tends to zero in metrics L-1. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

引用

页码：805 / 809

页数：5

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