Exponential behavior and upper noise excitation index of solutions to evolution equations with unbounded delay and tempered fractional Brownian motions

In this paper, we investigate stochastic evolution equations with unbounded delay in fractional power spaces perturbed by a tempered fractional Brownian motion Bσ,λQ(t) with −1/2<σ<0 and λ>0. We first introduce a technical lemma which is crucial in our stability analysis. Then, we prove the...

Descripción completa

Detalles Bibliográficos
Autores: Wang, Yejuan, Liu, Yarong, Caraballo Garrido, Tomás
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2021
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/116650
Acceso en línea:https://hdl.handle.net/11441/116650
https://doi.org/10.1007/s00028-020-00656-0
Access Level:acceso abierto
Palabra clave:Stochastic PDEs
Unbounded delay
Tempered fractional Brownian motion
Fractional powers of closed operators
Exponential decay in mean square
Descripción
Sumario:In this paper, we investigate stochastic evolution equations with unbounded delay in fractional power spaces perturbed by a tempered fractional Brownian motion Bσ,λQ(t) with −1/2<σ<0 and λ>0. We first introduce a technical lemma which is crucial in our stability analysis. Then, we prove the existence and uniqueness of mild solutions by using semigroup methods. The upper nonlinear noise excitation index of the energy solutions at any finite time t is also obtained. Finally, we consider the exponential asymptotic behavior of mild solutions in mean square.