Uniform trajectory attractor for non-autonomous reaction–diffusion equations with Carathéodory’s nonlinearity
We consider the problem of uniform long-time behavior of all globally defined weak solutions of a non-autonomous reaction–diffusion system with Carathéodory’s nonlinearity satisfying standard sign and polynomial growth assumptions. The main contributions of this paper are: (i) the existence of a uni...
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| Veröffentlicht in: | Nonlinear analysis 2014-03, Vol.98, p.13-26 |
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| container_title | Nonlinear analysis |
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| creator | Gorban, Nataliia V. Kapustyan, Oleksiy V. Kasyanov, Pavlo O. |
| description | We consider the problem of uniform long-time behavior of all globally defined weak solutions of a non-autonomous reaction–diffusion system with Carathéodory’s nonlinearity satisfying standard sign and polynomial growth assumptions. The main contributions of this paper are: (i) the existence of a uniform trajectory attractor for all globally defined weak solutions of non-autonomous reaction–diffusion equations with Carathéodory’s nonlinearity, (ii) sufficient conditions for the existence of a uniform trajectory attractor in strongest topologies, and (iii) new topological properties of weak solutions. |
| doi_str_mv | 10.1016/j.na.2013.12.004 |
| format | Article |
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| source | ScienceDirect Journals (5 years ago - present) |
| subjects | Carathéodory’s conditions Nonlinearity Polynomials Reaction-diffusion equations Reaction–diffusion system Topology Trajectories Uniform trajectory attractor |
| title | Uniform trajectory attractor for non-autonomous reaction–diffusion equations with Carathéodory’s nonlinearity |
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