On differential equations with delay in Banach spaces and attractors for retarded lattice dynamical systems
By Tomás Caraballo, Francisco Morillas, José Valero. 2013
72 citations recorded by the source corpus.
In this paper we first prove a rather general theorem about existence of solutions for an abstract differential equation in a Banach space by assuming that the nonlinear term is in some sense weakly continuous. We then apply this result to a lattice dynamical system with delay, proving also the existence of a global compact attractor for such system.
Subfields: Applied Mathematics, Computer Networks and Communications, Control and Systems Engineering
View Paper: https://www.semanticscholar.org/paper/fd44c89597eaf5ad754c1327e36e8fe90636de3a
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In Applied Mathematics
- Bixiang Wang
- Xiaoying Han
- Tomás Caraballo
- Xiaohu Wang
- Dingshi Li
- Pedro Marín-Rubio
- José Real
- Linfang Liu
In Computer Networks and Communications
- Bixiang Wang
- Xiaohu Wang
- Xiaoying Han
- Dingshi Li
- Tomás Caraballo
- Shengfan Zhou
- Kening Lu
- Pedro Marín-Rubio
In Control and Systems Engineering
- Bixiang Wang
- Xiaohu Wang
- Xiaoying Han
- Dingshi Li
- Tomás Caraballo
- Kening Lu
- Shengfan Zhou
- Pedro Marín-Rubio
Citations in the corpus
- A survey on Navier-Stokes models with delays: Existence, uniqueness and asymptotic behavior of solutions (2015, methodology): “Recent results on the theory of lattice dynamical systems with or without delays can be applied to the analysis of the lattice dynamical systems generated by the Navier-Stokes models ([27, 28], [46], [9, 10]).”
- Limiting Behavior of Invariant Measures of Stochastic Delay Lattice Systems (2021, background): “Recently, the solutions and their long-term dynamics of delay lattice systems have been considered in [12,14,23,36,44] in the deterministic case, and in [15,33,40,43] in the stochastic case.”