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Attractors for nonlinear reaction-diffusion systems in unbounded domains via the method of short trajectories |
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| Authors: | Maurizio Grasselli,Dalibor Pra?á k |
| Affiliation: | a Dipartimento di Matematica, Politecnico di Milano, Via Bonardi 9, I-20133 Milano, Italy b Katedra matematické analýzy, Matematicko-fyzikální fakulta Univerzity Karlovy, Sokolovská 83, CZ-186 75, Czech Republic c Dipartimento di Matematica, Università di Pavia, Via Ferrata, 1, I-27100 Pavia, Italy |
| Abstract: | We consider a nonlinear reaction-diffusion equation on the whole space Rd. We prove the well-posedness of the corresponding Cauchy problem in a general functional setting, namely, when the initial datum is uniformly locally bounded in L2 only. Then we adapt the short trajectory method to establish the existence of the global attractor and, if d?3, we find an upper bound of its Kolmogorov's ε-entropy. |
| Keywords: | 35B41 35K57 92D25 |
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