A nonlinear semigroup approach to Hamilton-Jacobi equations-revisited

被引：0

作者：

Ni, Panrui ^{[1
]}

Wang, Lin ^{[2
]}

机构：

[1] Fudan Univ, Shanghai Ctr Math Sci, Shanghai 200438, Peoples R China

[2] Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2024年 / 403卷

关键词：

Aubry-Mather theory; Weak KAM theory; Hamiltonian systems; Contact Hamiltonian systems; LARGE TIME BEHAVIOR; VISCOSITY SOLUTIONS; CONVERGENCE;

D O I：

10.1016/j.jde.2024.05.039

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the Hamilton-Jacobi equation H (x, Du) + lambda(x)u = c, x is an element of M, where M is a connected, closed and smooth Riemannian manifold. The functions H (x, p) and lambda(x) are continuous. H (x, p) is convex, coercive with respect to p , and lambda(x) changes the signs. The first breakthrough to this model was achieved by Jin-Yan-Zhao [11] under the Tonelli conditions. In this paper, we consider more detailed structure of the viscosity solution set and large time behavior of the viscosity solution on the Cauchy problem. To the best of our knowledge, it is the first detailed description of the large time behavior of the HJ equations with non-monotone dependence on the unknown function. (c) 2024 Published by Elsevier Inc.

引用

页码：272 / 307

页数：36

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