Set-valued solutions to the Cauchy problem for hyperbolic systems of partial differential inclusions

被引：15

作者：

Aubin, Jean-Pierre ^{[1
]}

Frankowska, Halina ^{[1
]}

机构：

[1] Univ Paris 09, CEREMADE, F-75775 Paris 16, France

来源：

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 1997年 / 4卷 / 02期

关键词：

Differential Equation; Partial Differential Equation; Ordinary Differential Equation; Cauchy Problem; Control Theory;

D O I：

10.1007/PL00001413

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the existence of global set-valued solutions to the Cauchy problem for partial differential equations and inclusions, with either single-valued or set-valued initial conditions. The method is based on the equivalence between this problem and problem of finding viability tubes of the associated characteristic system of ordinary differential equations. As an application we construct the value function of the Mayer problem arising in control theory.

引用

页码：149 / 168

页数：20

共 15 条

[1] [Anonymous], SHOCKS WAVES REACTIO
[2] Aubin J.-P., 1991, Viability Theory
[3] Aubin J.-P., 1990, Set-valued analysis, DOI 10.1007/978-0-8176-4848-0
[4] Aubin J. P., 1984, Differential inclusions: Set-valued maps and viability theory
[5] Aubin J.-P., J CONVEX AN IN PRESS
[6] AUBIN J.-P., 1991, ANN SCUOLA NORM PISA, V18, P541
[7] AUBIN JP, 1990, CR ACAD SCI I-MATH, V311, P851
[8] AUBIN JP, 1990, CR ACAD SCI I-MATH, V311, P295
[9] AUBIN JP, 1991, CR ACAD SCI I-MATH, V312, P271
[10] AUBIN JP, 1981, ADV MATH S, P160

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