dc.creator | NGuyen, Huy Tuan | es |
dc.creator | Caraballo Garrido, Tomás | es |
dc.creator | Thach, Tran Ngoc | es |
dc.date.accessioned | 2023-07-12T09:23:43Z | |
dc.date.available | 2023-07-12T09:23:43Z | |
dc.date.issued | 2022-10-06 | |
dc.identifier.citation | NGuyen, H.T., Caraballo Garrido, T. y Thach, T.N. (2022). New results for stochastic fractional pseudo-parabolic equations with delays driven by fractional Brownian motion. Stochastic Processes and their Applications, 161, 24-67. https://doi.org/10.1016/j.spa.2023.03.012. | |
dc.identifier.issn | 0304-4149 | es |
dc.identifier.issn | 1879-209X | es |
dc.identifier.uri | https://hdl.handle.net/11441/147894 | |
dc.description.abstract | In this work, four problems for stochastic fractional pseudo-parabolic containing bounded
and unbounded delays are investigated. The fractional derivative and the stochastic noise we consider here are the Caputo operator and the fractional Brownian motion. For the two problems
involving bounded delays, we aim at establishing global existence, uniqueness, and regularity results
under integral Lipschitz conditions for the non-linear source terms. Such behaviors of mild solutions
are also analyzed in the unbounded delay cases but under globally and locally Lipschitz assumptions. We emphasize that our results are investigated in the novel spaces C([−r, T];L
p
(Ω, Wl,q(D))),
Cµ((−∞, T];L
p
(Ω, Wl,q(D))), and the weighted space F
ε
µ((−∞, T];L
p
(Ω, Wl,q(D))), instead of usual
ones C([−r, T];L
2
(Ω, H)), Cµ((−∞, T];L
2
(Ω, H)). The main technique allowing us to overcome the
rising difficulties lies on some useful Sobolev embeddings between the Hilbert space H = L
2
(D) and
Wl,q(D), and some well-known fractional tools. In addition, we also study the H¨older continuity for
the mild solutions, which can be considered as one of the main novelties of this paper. Finally, we
consider an additional result connecting delay stochastic fractional pseudo-parabolic equations and
delay stochastic fractional parabolic equations. We show that the mild solution of the first model
converges to the mild solution of the second one, in some sense, as the diffusion parameter β → 0
+. | es |
dc.format | application/pdf | es |
dc.format.extent | 43 p. | es |
dc.language.iso | eng | es |
dc.publisher | Elsevier | es |
dc.relation.ispartof | Stochastic Processes and their Applications, 161, 24-67. | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | fractional pseudo-parabolic equations | es |
dc.subject | fractional Brownian motion | es |
dc.subject | bounded delay | es |
dc.subject | unbounded delay | es |
dc.subject | stochastic fractional differential equations | es |
dc.title | New results for stochastic fractional pseudo-parabolic equations with delays driven by fractional Brownian motion | 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/10.1016/j.spa.2023.03.012 | es |
dc.identifier.doi | 10.1016/j.spa.2023.03.012 | es |
dc.contributor.group | Universidad de Sevilla. FQM314: Análisis Estocástico de Sistemas Diferenciales | es |
dc.journaltitle | Stochastic Processes and their Applications | es |
dc.publication.volumen | 161 | es |
dc.publication.initialPage | 24 | es |
dc.publication.endPage | 67 | es |