Initial data identification in space dependent conservation laws and Hamilton-Jacobi equations

被引：1

作者：

Colombo, Rinaldo M. ^{[1
,2
]}

Perrollaz, Vincent ^{[3
]}

Sylla, Abraham ^{[4
]}

机构：

[1] Univ Brescia, INdAM Unit, Brescia, Italy

[2] Univ Brescia, Dept Informat Engn, Brescia, Italy

[3] Univ Orleans, Univ Tours, CNRS UMR 7013, Inst Denis Poisson, Orleans, France

[4] Univ Milano Bicocca, Dept Math & Applicat, Milan, Italy

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2024年 / 49卷 / 5-6期

关键词：

Inverse design for hyperbolic equations; Conservation Laws; Hamilton-Jacobi equation; optimal control problem; VISCOSITY SOLUTIONS; ATTAINABLE SET; SINGULARITIES; SYSTEMS;

D O I：

10.1080/03605302.2024.2348047

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Consider a Conservation Law and a Hamilton-Jacobi equation with a flux/Hamiltonian depending also on the space variable. We characterize first the attainable set of the two equations and, second, the set of initial data evolving at a prescribed time into a prescribed profile. An explicit example then shows the deep differences between the cases of x-independent and x-dependent fluxes/Hamiltonians.

引用

页码：470 / 504

页数：35

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