Article
Well-posedness and dynamics of impulsive fractional stochastic evolution equations with unbounded delay
Author/s | Xu, Jiaohui
Zhang, Zhengce Caraballo Garrido, Tomás |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2019-08 |
Deposit Date | 2019-04-12 |
Published in |
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Abstract | This paper is concerned with the well-posedness and dynamics of delay impulsive fractional stochastic evolution equations with time fractional differential operator α ∈ (0, 1). After establishing the well-posedness of the ... This paper is concerned with the well-posedness and dynamics of delay impulsive fractional stochastic evolution equations with time fractional differential operator α ∈ (0, 1). After establishing the well-posedness of the problem, and a result ensuring the existence and uniqueness of mild solutions globally defined in future, the existence of a minimal global attracting set is investigated in the mean-square topology, under general assumptions not ensuing the uniqueness of solutions. Furthermore, in the case of uniqueness, it is possible to provide more information about the geometrical structure of such global attracting set. In particular, it is proved that the minimal compact globally attracting set for the solutions of the problem becomes a singleton. It is remarkable that the attraction property is proved in the usual forward sense, unlike the pullback concept used in the context of random dynamical systems, but the main point is that the model under study has not been proved to generate a random dynamical system. |
Project ID. | 11371286
MTM2015-63723-P P12-FQM-1492 |
Citation | Xu, J., Zhang, Z. y Caraballo Garrido, T. (2019). Well-posedness and dynamics of impulsive fractional stochastic evolution equations with unbounded delay. Communications in Nonlinear Science and Numerical Simulation, 75, 121-139. |
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