dc.creator | Xu, Jiaohui | es |
dc.creator | Caraballo Garrido, Tomás | es |
dc.date.accessioned | 2022-09-30T08:43:14Z | |
dc.date.available | 2022-09-30T08:43:14Z | |
dc.date.issued | 2022 | |
dc.identifier.citation | Xu, J. y Caraballo Garrido, T. (2022). Long Time Behavior of Stochastic Nonlocal Partial Differential Equations and Wong--Zakai Approximations. SIAM Journal on Mathematical Analysis (SIMA), 54, 3-1-3-46. | |
dc.identifier.issn | 0036-1410 | es |
dc.identifier.issn | 1095-7154 | es |
dc.identifier.uri | https://hdl.handle.net/11441/137511 | |
dc.description.abstract | This paper is devoted to investigating the well-posedness and asymptotic behavior of a class of stochastic
5 nonlocal partial differential equations driven by nonlinear noise. First, the existence of a weak martingale solution is estab 6 lished by using the Faedo-Galerkin approximation and an idea analogous to Da Prato and Zabczyk [12]. Second, we show
7 the uniqueness and continuous dependence on initial values of solutions to the above stochastic nonlocal problem when there
8 exist some variational solutions. Third, the asymptotic local stability of steady-state solutions is analyzed either when the
9 steady-state solutions of the deterministic problem is also solution of the stochastic one, or when this does not happen. Next,
10 to study the global asymptotic behavior, namely, the existence of attracting sets of solutions, we consider an approximation
11 of the noise given by Wong-Zakai’s technique using the so called colored noise. For this model, we can use the power of
12 the theory of random dynamical systems and prove the existence of random attractors. Eventually, particularizing in the
13 cases of additive and multiplicative noise, it is proved that the Wong-Zakai approximation models possess random attractors
14 which converge upper-semicontinuously to the respective random attractors of the stochastic equations driven by standard
15 Brownian motions. This fact justifies the use of this colored noise technique to approximate the asymptotic behavior of the
16 models with general nonlinear noises, although the convergence of attractors and solutions is still an open problem. | es |
dc.format | application/pdf | es |
dc.format.extent | 46 p. | es |
dc.language.iso | eng | es |
dc.publisher | SIAM | es |
dc.relation.ispartof | SIAM Journal on Mathematical Analysis (SIMA), 54, 3-1-3-46. | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | Nonlinear stochastic term | es |
dc.subject | Colored noise | es |
dc.subject | Variational solutions | es |
dc.subject | Steady-state solution | es |
dc.subject | Attractors | es |
dc.subject | Upper 18 semi-continuity | es |
dc.title | Long Time Behavior of Stochastic Nonlocal Partial Differential Equations and Wong--Zakai Approximations | es |
dc.type | info:eu-repo/semantics/article | es |
dcterms.identifier | https://ror.org/03yxnpp24 | |
dc.type.version | info:eu-repo/semantics/submittedVersion | es |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es |
dc.contributor.affiliation | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico | es |
dc.relation.publisherversion | https://doi.org/10.1137/21M1412645 | es |
dc.identifier.doi | 10.1137/21M1412645 | es |
dc.journaltitle | SIAM Journal on Mathematical Analysis (SIMA) | es |
dc.publication.volumen | 54 | es |
dc.publication.initialPage | 3-1 | es |
dc.publication.endPage | 3-46 | es |