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

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