We consider a nonlinear reaction–diffusion equation on the whole space R^d. 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 L^2 only. Then we adapt the short trajectory method to establish the existence of the global attractor and, if the d < 4, we find an upper bound of its Kolmogorov’s epsilon-entropy.
Attractors for nonlinear reaction-diffusion systems in unbounded domains via the method of short trajectories
GRASSELLI, MAURIZIO;
2010-01-01
Abstract
We consider a nonlinear reaction–diffusion equation on the whole space R^d. 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 L^2 only. Then we adapt the short trajectory method to establish the existence of the global attractor and, if the d < 4, we find an upper bound of its Kolmogorov’s epsilon-entropy.File in questo prodotto:
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