Artículo
Dynamics of stochastic nonlocal partial differential equations
Autor/es | Xu, Jiaohui
Caraballo Garrido, Tomás |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2021-08-17 |
Fecha de depósito | 2022-03-03 |
Publicado en |
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Resumen | This paper is concerned with the asymptotic behavior of solutions to nonlocal stochastic partial differential equations with multiplicative and additive noise driven by a standard Brownian motion, respectively. First of ... This paper is concerned with the asymptotic behavior of solutions to nonlocal stochastic partial differential equations with multiplicative and additive noise driven by a standard Brownian motion, respectively. First of all, the stochastic nonlocal differential equations are transformed into their associated conjugated random differential equations, we then construct the dynamical systems to the original problems via the properties of conjugation. Next, in the case of multiplicative noise, we establish the existence of the random attractor when it absorbs every bounded deterministic set. Particularly, it is shown the pullback random attractor, which is also forward attracting, becomes a singleton when the external forcing term vanishes at zero. Eventually, in the case of additive noise, two approaches are applied to prove the existence of pullback random attractors with the help of energy estimations. Actually, these two attractors turn out to be the same one. |
Cita | Xu, J. y Caraballo Garrido, T. (2021). Dynamics of stochastic nonlocal partial differential equations. The European Physical Journal Plus, 136 (8), 849-1-849-33. |
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