Non-autonomous nonlocal partial differential equations with delay and memory
The paper addresses a kind of non-autonomous nonlocal parabolic equations when the external force contains hereditary characteristics involving bounded and unbounded delays. First, well-posedness of the problem is analyzed by the Galerkin method and energy estimations in the phase space Cρ(X). Moreo...
| Authors: | , , |
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| Format: | article |
| Status: | Versión aceptada para publicación |
| Publication Date: | 2020 |
| Country: | España |
| Institution: | Universidad de Sevilla (US) |
| Repository: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/104537 |
| Online Access: | https://hdl.handle.net/11441/104537 https://doi.org/10.1016/j.jde.2020.07.037 |
| Access Level: | Open access |
| Keyword: | Non-autonomous nonlocal parabolic equations Bounded and unbounded delays Stationary solutions Pullback attractors |
| Summary: | The paper addresses a kind of non-autonomous nonlocal parabolic equations when the external force contains hereditary characteristics involving bounded and unbounded delays. First, well-posedness of the problem is analyzed by the Galerkin method and energy estimations in the phase space Cρ(X). Moreover, some results related to strong solutions are proved under suitable assumptions. The existence of stationary solutions is then established by a corollary of the Brower fixed point theorem. By constructing appropriate Lyapunov functionals in terms of the characteristic delay terms, a deep analysis on stability and attractive-ness of the stationary solutions is established. Furthermore, the existence of pullback attractors in L2( ), with bounded and unbounded delays, is shown. We emphasize that, to prove the existence of pullback attractors in the unbounded delay case, a new phase space, Eγ, has to be constructed. |
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