A new PDE approach to the large time asymptotics of solutions of Hamilton-Jacobi equations

被引：10

作者：

Barles, Guy ^{[1
]}

Ishii, Hitoshi ^{[2
,3
]}

Mitake, Hiroyoshi ^{[4
]}

机构：

[1] Univ Tours, CNRS, Lab Math & Phys Theor, UMR 7350,FR 2964, F-37200 Tours, France

[2] Waseda Univ, Fac Educ & Integrated Arts & Sci, Shinjuku Ku, Tokyo 1698050, Japan

[3] King Abdulaziz Univ, Fac Sci, Jeddah 21589, Saudi Arabia

[4] Fukuoka Univ, Dept Appl Math, Fac Sci, Fukuoka 8140180, Japan

来源：

BULLETIN OF MATHEMATICAL SCIENCES | 2013年 / 3卷 / 03期

关键词：

Asymptotic behavior; Hamilton-Jacobi equations; PDE approach; EUCLIDEAN-N-SPACE; BEHAVIOR;

D O I：

10.1007/s13373-013-0036-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce a new PDE approach to establishing the large time asymptotic behavior of solutions of Hamilton-Jacobi equations, which modifies and simplifies the previous ones (Barles et al. in Arch Ration Mech Anal 204(2):515-558, 2012; Barles and Souganidis in SIAM J Math Anal 31(4):925-939, 2000), under a refined "strict convexity" assumption on the Hamiltonians. Not only such "strict convexity" conditions generalize the corresponding requirements on the Hamiltonians in Barles and Souganidis (SLAM J Math Anal 31(4):925-939, 2000), but also one of the most refined our conditions covers the situation studied in Namah and Roquejoffre (Commun Partial Differ Equ 24(5-6):883-893, 1999).

引用

页码：363 / 388

页数：26

共 19 条

[1]

BARLES G, 1985, ANN I H POINCARE-AN, V2, P21

[2] On the large time behavior of solutions of Hamilton-Jacobi equations [J].

Barles, G ;

Souganidis, PE .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2000, 31 (04) :925-939

[3]

Barles G., 1994, MATH APPL BERLIN, V17

[4] On the Large Time Behavior of Solutions of Hamilton-Jacobi Equations Associated with Nonlinear Boundary Conditions [J].

Barles, Guy ;

Ishii, Hitoshi ;

Mitake, Hiroyoshi .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2012, 204 (02) :515-558

[5] A PDE Approach to Large-Time Asymptotics for Boundary-Value Problems for Nonconvex Hamilton-Jacobi Equations [J].

Barles, Guy ;

Mitake, Hiroyoshi .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2012, 37 (01) :136-168

[6]

Cagnetti F., ARXIV12124694

[7] USERS GUIDE TO VISCOSITY SOLUTIONS OF 2ND-ORDER PARTIAL-DIFFERENTIAL EQUATIONS [J].

CRANDALL, MG ;

ISHII, H ;

LIONS, PL .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1992, 27 (01) :1-67

[8] A generalized dynamical approach to the large time behavior of solutions of Hamilton-Jacobi equations [J].

Davini, Andrea ;

Siconolfi, Antonio .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2006, 38 (02) :478-502

[9] On convergence of the Lax-Oleinik semi-group [J].

Fathi, A .

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1998, 327 (03) :267-270

[10] Asymptotic solutions of Hamilton-Jacobi equations in Euclidean n space [J].

Fujita, Yasuhiro ;

Ishii, Hitoshi ;

Loreti, Paola .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2006, 55 (05) :1671-1700

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