FINITE-TIME CONVERGENCE OF SOLUTIONS OF HAMILTON-JACOBI EQUATIONS

被引：1

作者：

Wang, Kaizhi ^{[1
]}

Yan, Jun ^{[2
]}

Zhao, Kai ^{[2
]}

机构：

[1] Shanghai Jiao Tong Univ, Sch Math Sci, Shanghai 200240, Peoples R China

[2] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2022年 / 150卷 / 03期

关键词：

Hamilton-Jacobi equations; viscosity solutions; finite-time convergence; weak KAM theory; VISCOSITY SOLUTIONS;

D O I：

10.1090/proc/15736

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with the long-time behavior of viscosity solutions of evolutionary contact Hamilton-Jacobi equations w(t) + H(x, w, w(x)) = 0, where H(x, u, p) is strictly decreasing in u and satisfies Tonelli conditions in p. We show that each viscosity solution of the ergodic contact Hamilton-Jacobi equation H(x, u, u(x)) = 0 can be reached by many different viscosity solutions of the above evolutionary equation in a finite time.

引用

页码：1187 / 1196

页数：10

共 11 条

[1]

[Anonymous], 2008, The Weak KAM Theorem in Lagrangian Dynamics

[2]

Cannarsa P., 2019, Trends in Control Theory and Partial Differential Equations, V32, P39, DOI [10.1007/978-3-030-17949-63, DOI 10.1007/978-3-030-17949-63]

[3] Herglotz' variational principle and Lax-Oleinik evolution [J].

Cannarsa, Piermarco ;

Cheng, Wei ;

Jin, Liang ;

Wang, Kaizhi ;

Yan, Jun .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2020, 141 :99-136

[4] SOME PROPERTIES OF VISCOSITY SOLUTIONS OF HAMILTON-JACOBI EQUATIONS [J].

CRANDALL, MG ;

EVANS, LC ;

LIONS, PL .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1984, 282 (02) :487-502

[5] VISCOSITY SOLUTIONS OF HAMILTON-JACOBI EQUATIONS [J].

CRANDALL, MG ;

LIONS, PL .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 277 (01) :1-42

[6]

Fathi A, 2014, PROCEEDINGS OF THE INTERNATIONAL CONGRESS OF MATHEMATICIANS (ICM 2014), VOL III, P597

[7]

Ishii Hitoshi, 2006, Eur. Math. Soc., VIII, P213

[8] Weak KAM solutions of Hamilton-Jacobi equations with decreasing dependence on unknown functions [J].

Wang, Kaizhi ;

Wang, Lin ;

Yan, Jun .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 286 :411-432

[9] Aubry-Mather Theory for Contact Hamiltonian Systems [J].

Wang, Kaizhi ;

Wang, Lin ;

Yan, Jun .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2019, 366 (03) :981-1023

[10] Variational principle for contact Hamiltonian systems and its applications [J].

Wang, Kaizhi ;

Wang, Lin ;

Yan, Jun .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2019, 123 :167-200

← 1 2 →