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

Yasuhiro Fujita; Hitoshi Ishii; Paola Loreti

doi:10.1080/03605300500358087

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

Yasuhiro Fujita, Hitoshi Ishii^*, Paola Loreti

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

22 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 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.

Original language	English
Pages (from-to)	827-848
Number of pages	22
Journal	Communications in Partial Differential Equations
Volume	31
Issue number	6
DOIs	https://doi.org/10.1080/03605300500358087
Publication status	Published - 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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10.1080/03605300500358087

Cite this

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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.",

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AU - Fujita, Yasuhiro

AU - Ishii, Hitoshi

AU - Loreti, Paola

PY - 2006/6

Y1 - 2006/6

N2 - 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.

AB - 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.

KW - Long time behavior

KW - Maximum principle

KW - Ornstein-Uhlenbeck operator

KW - Viscosity solutions

KW - Viscous Hamilton-Jacobi equations

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

Abstract

Keywords

ASJC Scopus subject areas

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