Asymptotic solutions of viscous hamilton- jacobi equations with ornstein-uhlenbeck operator

Yasuhiro Fujita, Hitoshi Ishii, Paola Loreti

    Research output: Contribution to journalArticle

    18 Citations (Scopus)

    Abstract

    We study the long time behavior of solutions of the Cauchy problem for semilinear parabolic equations with the Ornstein-Uhlenbeck operator in ℝN. 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.

    Original languageEnglish
    Pages (from-to)827-848
    Number of pages22
    JournalCommunications in Partial Differential Equations
    Volume31
    Issue number6
    DOIs
    Publication statusPublished - 2006 Jun

    Keywords

    • Long time behavior
    • Maximum principle
    • Ornstein-Uhlenbeck operator
    • Viscosity solutions
    • Viscous Hamilton-Jacobi equations

    ASJC Scopus subject areas

    • Mathematics(all)
    • Analysis
    • Applied Mathematics

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