scholarly journals On the Kneser property for reaction–diffusion systems on unbounded domains

2009 ◽  
Vol 156 (18) ◽  
pp. 3029-3040 ◽  
Author(s):  
Francisco Morillas ◽  
José Valero
Keyword(s):  
Unbounded Domains ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems

Global and exponential attractors for nonlinear reaction–diffusion systems in unbounded domains

2004 ◽  
Vol 134 (2) ◽  
pp. 271-315 ◽  
Author(s):  
M. Efendiev ◽  
A. Miranville ◽  
S. Zelik
Keyword(s):  
Unbounded Domains ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Exponential Attractors ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Long Time ◽  
Entropy Estimate ◽  
External Forces ◽  
Kolmogorov's Entropy

We study the long-time behaviour of solutions of autonomous and non-autonomous reaction-diffusion equations in unbounded domains of R3. It is shown that, under appropriate assumptions on the nonlinear interaction function and on the external forces, these equations possess compact global (uniform) attractors in the corresponding phase space. Estimates for Kolmogorov's ε-entropy of these attractors in terms of Kolmogorov's entropy of the external forces are given. Moreover, (infinite-dimensional) exponential attractors with the same entropy estimate as that of the corresponding global (uniform) attractor are also constructed.

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