Asymptotic Solutions of Viscous Hamilton–Jacobi Equations with Ornstein–Uhlenbeck Operator
Asymptotic Solutions of Viscous Hamilton–Jacobi Equations with Ornstein–Uhlenbeck Operator
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DOI：
10.1080/03605300500358087
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发表时间：
2006-07
影响因子：
1.9
通讯作者：
Y. Fujita;H. Ishii;P. Loreti
中科院分区：
文献类型：
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作者：
Y. Fujita;H. Ishii;P. Loreti
本文研究了具有Ornstein-Uhlenbeck算子的半线性抛物方程Cauchy问题解的长时间性态。主要结果中的长时间性态是借助于对应于遍历问题来描述的，它补充了Namah（1996），Namah and Roquejoffre（1999），Roquejoffre（1998），Fathi（1998），Barles和Souganovich（2000 - 2001）。我们还建立了半线性抛物方程的Cauchy问题和遍历问题的解的存在性和唯一性结果与Ornstein-Uhlenbeck算子。
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.