Large time behavior of solutions of viscous Hamilton-Jacobi equations with superquadratic Hamiltonian

被引：32

作者：

Tchamba, Thierry Tabet ^{[1
,2
]}

机构：

[1] Univ Tours, Lab Math & Phys Theor, CNRS, UMR 6083,FR 2964, Tours, France

[2] Univ Yaounde I, Dept Math, Yaounde, Cameroon

来源：

ASYMPTOTIC ANALYSIS | 2010年 / 66卷 / 3-4期

关键词：

NONLINEAR ELLIPTIC-EQUATIONS; STRONG MAXIMUM PRINCIPLE; VISCOSITY SOLUTIONS; DIRICHLET PROBLEM; GLOBAL EXISTENCE; CAUCHY-PROBLEM; DECAY; DOMAINS;

D O I：

10.3233/ASY-2009-0965

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the long-time behavior of the unique viscosity solution u of the viscous Hamilton-Jacobi equation u(t) - Delta u + |Du|(m) = f in Omega x (0,+infinity) with inhomogeneous Dirichlet boundary conditions, where Omega is a bounded domain of R-N. We mainly focus on the superquadratic case (m > 2) and consider the Dirichlet conditions in the generalized viscosity sense. Under rather natural assumptions on f, the initial and boundary data, we connect the problem studied to its associated stationary generalized Dirichlet problem on one hand and to a stationary problem with a state constraint boundary condition on the other hand.

引用

页码：161 / 186

页数：26

共 50 条

[41] Asymptotic solutions for large time of Hamilton-Jacobi equations in Euclidean n space
Ishii, Hitoshi
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2008, 25 (02): : 231 - 266
[42] A new PDE approach to the large time asymptotics of solutions of Hamilton-Jacobi equations
Barles, Guy
Ishii, Hitoshi
Mitake, Hiroyoshi
BULLETIN OF MATHEMATICAL SCIENCES, 2013, 3 (03) : 363 - 388
[43] Global solutions to viscous Hamilton-Jacobi equations with irregular initial data
Benachour, S
Laurençot, P
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1999, 24 (11-12) : 1999 - 2021
[44] An asymptotic analysis for Hamilton-Jacobi equations with large Hamiltonian drift terms
Kumagai, Taiga
ADVANCES IN CALCULUS OF VARIATIONS, 2021, 14 (01) : 63 - 81
[45] Null controllability of viscous Hamilton-Jacobi equations
Porretta, Alessio
Zuazua, Enrique
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2012, 29 (03): : 301 - 333
[46] Semiconcavity estimates for viscous Hamilton-Jacobi equations
Stromberg, Thomas
ARCHIV DER MATHEMATIK, 2010, 94 (06) : 579 - 589
[47] On unbounded solutions of ergodic problems in m for viscous Hamilton-Jacobi equations
Barles, Guy
Meireles, Joao
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2016, 41 (12) : 1985 - 2003
[48] Non-Diffusive Large Time Behavior for a Degenerate Viscous Hamilton-Jacobi Equation
Laurencot, Philippe
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2009, 34 (03) : 281 - 304
[49] SOME RESULTS FOR THE LARGE TIME BEHAVIOR OF HAMILTON-JACOBI EQUATIONS WITH CAPUTO TIME DERIVATIVE
Ley, Olivier
Topp, Erwin
Yangari, Miguel
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2021, 41 (08) : 3555 - 3577
[50] A dynamical approach to the large-time behavior of solutions to weakly coupled systems of Hamilton-Jacobi equations
Mitake, H.
Tran, H. V.
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2014, 101 (01): : 76 - 93

← 1 2 3 4 5 →