Generation of singularities from the initial datum for Hamilton-Jacobi equations

被引：3

作者：

Albano, Paolo ^{[1
]}

Cannarsa, Piermarco ^{[2
]}

Sinestrari, Carlo ^{[3
]}

机构：

[1] Univ Bologna, Dipartimento Matemat, Piazza Porta San Donato 5, I-40127 Bologna, Italy

[2] Univ Roma Tor Vergata, Dipartimento Matemat, Via Ric Sci, I-00133 Rome, Italy

[3] Univ Roma Tor Vergata, Dipartimento Ingn Civile & Ingn Informat, Via Politecn, I-00133 Rome, Italy

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2020年 / 268卷 / 04期

关键词：

Hamilton-Jacobi equations; Viscosity solutions; Singularities; Generalized characteristics; VISCOSITY SOLUTIONS; GLOBAL PROPAGATION; DYNAMICS;

D O I：

10.1016/j.jde.2019.08.051

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the generation of singularities from the initial datum for a solution of the Cauchy problem for a class of Hamilton-Jacobi equations of evolution. For such equations, we give conditions for the existence of singular generalized characteristics starting at the initial time from a given point of the domain, depending on the properties of the proximal subdifferential of the initial datum in a neighbourhood of that point. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：1412 / 1426

页数：15

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