Asymptotic solutions of viscous Hamilton-Jacobi equations with Ornstein-Uhlenbeck operator

被引：26

作者：

Fujita, Yasuhiro

Ishii, Hitoshi ^{[1
]}

Loreti, Paola

机构：

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

[2] Toyama Univ, Dept Math, Toyama 930, Japan

[3] Univ Roma La Sapienza, Dipartimento Metodi & Modeli Matemat Sci Applicat, Rome, Italy

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2006年 / 31卷 / 06期

关键词：

long time behavior; maximum principle; Ornstein-Uhlenbeck operator; viscosity solutions; viscous Hamilton-Jacobi equations;

D O I：

10.1080/03605300500358087

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 solutions of the Cauchy problem for semilinear parabolic equations with the Ornstein-Uhlenbeck operator in R-N . The long time behavior in the main results is stated with help of the corresponding to ergodic problem, which complements, in the case of unbounded domains, the recent developments on long time behaviors of solutions of (viscous) Hamilton-Jacobi equations due to Namah (1996), Namah and Roquejoffre (1999), Roquejoffre (1998), Fathi (1998), Barles and Souganidis (2000, 2001). We also establish existence and uniqueness results for solutions of the Cauchy problem and ergodic problem for semilinear parabolic equations with the Ornstein-Uhlenbeck operator.

引用

页码：827 / 848

页数：22

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