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Article Dans Une Revue Communications in Pure and Applied Analysis Année : 2019

Large time behavior of solutions of local and nonlocal nondegenerate Hamilton-Jacobi equations with Ornstein-Uhlenbeck operator

Résumé

We study the well-posedness of second order Hamilton-Jacobi equations with an Ornstein-Uhlenbeck operator in R N and R N ×[0, +∞). As applications, we solve the associated ergodic problem associated to the stationary equation and obtain the large time behavior of the solutions of the evolution equation when it is nondegenerate. These results are some generalizations of the ones obtained by Fujita, Ishii & Loreti (2006) by considering more general diffusion matrices or nonlocal operators of integro-differential type and general sublinear Hamiltonians. Our work uses as a key ingredient the a-priori Lipschitz estimates obtained in Chasseigne, Ley & Nguyen (2017).
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Dates et versions

hal-01533664 , version 2 (21-03-2018)
hal-01533664 , version 3 (27-03-2019)

Identifiants

  • HAL Id : hal-01533664 , version 2

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Thi-Tuyen Nguyen. Large time behavior of solutions of local and nonlocal nondegenerate Hamilton-Jacobi equations with Ornstein-Uhlenbeck operator. Communications in Pure and Applied Analysis, 2019. ⟨hal-01533664v2⟩
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