scholarly journals Attractor of reaction-diffusion equations in Banach spaces

2001 ◽  
Vol 2 (1) ◽  
pp. 77
Author(s):  
José Valero
Keyword(s):  
Fractal Dimension ◽  
Phase Space ◽  
Banach Spaces ◽  
Global Attractor ◽  
Differential Inclusions ◽  
Reaction Diffusion ◽  
Global Attractors ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Dissipative Operators

In this paper we prove first some abstract theorems on existence of global attractors for differential inclusions generated by w-dissipative operators. Then these results are applied to reaction-diffusion equations in which the Babach space L<sub>p </sub>is used as phase space. Finally, new results concerning the fractal dimension of the global attractor in the space L<sub>2</sub> are obtained.<br /><sub> </sub>

scholarly journals Exponential Attractor for a First-Order Dissipative Lattice Dynamical System

2008 ◽  
Vol 2008 ◽  
pp. 1-8 ◽  
Author(s):  
Xiaoming Fan
Keyword(s):  
Dynamical System ◽  
Fractal Dimension ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Exponential Attractor ◽  
Spatial Discretization ◽  
First Order ◽  
Lattice Dynamical System

We construct an exponential attractor for a first-order dissipative lattice dynamical system arising from spatial discretization of reaction-diffusion equations in . And we obtain fractal dimension of the exponential attractor.

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