Long-time dynamics of a second-order non-autonomous multi-valued stochastic lattice model with bounded variable and unbounded distributed delays (original) (raw)
Abstract
In this study, we explore the long-time dynamics of second-order non-autonomous multi-valued stochastic lattice systems characterized by varying coefficients, discrete and unbounded distributed delays. Instead of imposing Lipschitz continuity for the nonlinear terms of the resulting system, we adopt a weaker continuity assumption accompanied by growth conditions, which results in the non-uniqueness of solutions to the associated Cauchy problem. With the lack of Lipschitz conditions, we investigate the global existence of solutions for the system, which generates a multi-valued cocycle. Furthermore, the existence of the pullback attractor is considered. With the combined effects of varying coefficients, multiplicative noise and complex delays, the pullback attractor is time-dependent in the time-dependent phase space in which can be substantiated the well-posedness.
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Funding
This research was supported by NSF of China (12201176), NSF of Hebei Province (A2022205031), the Youth Talent Project of Hebei Educational Committee (BJ2025026) and the Key Postdoctoral Talent Project of Hebei Province (B2024003005) and the Spanish Ministerio de Ciencia, Innovación (AEI) y Universidades, AEI and FEDER under project PID2024-156228NB-I00.
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Author notes
- Meiyu Sui and Jia Hao contributed equally to this work.
Authors and Affiliations
- School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, 050024, China
Meiyu Sui & Jia Hao - Depto. Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, c/ Tarfia s/n, 41012, Sevilla, Spain
Tomás Caraballo
Authors
- Meiyu Sui
- Jia Hao
- Tomás Caraballo
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Correspondence toTomás Caraballo.
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Sui, M., Hao, J. & Caraballo, T. Long-time dynamics of a second-order non-autonomous multi-valued stochastic lattice model with bounded variable and unbounded distributed delays.Comp. Appl. Math. 45, 64 (2026). https://doi.org/10.1007/s40314-025-03455-w
- Received: 25 April 2025
- Revised: 19 September 2025
- Accepted: 20 September 2025
- Published: 15 October 2025
- Version of record: 15 October 2025
- DOI: https://doi.org/10.1007/s40314-025-03455-w