scholarly journals The existence of global attractors for a class of reaction–diffusion equations with distribution derivatives terms in Rn

2015 ◽  
Vol 427 (1) ◽  
pp. 365-376
Author(s):  
Jin Zhang ◽  
Chengkui Zhong
Keyword(s):  
Reaction Diffusion ◽  
Global Attractors ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations

scholarly journals On Lr-regularity of global attractors generated by strong solutions of reaction-diffusion equations

2016 ◽  
Vol 1 (2) ◽  
pp. 375-390 ◽  
Author(s):  
José Valero
Keyword(s):  
Nonlinear Term ◽  
Mild Solutions ◽  
Reaction Diffusion ◽  
Strong Solutions ◽  
Global Attractors ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Reaction Diffusion Equation ◽  
The Cauchy Problem ◽  
Weak Attractor

AbstractIn this paper we prove that the global attractor generated by strong solutions of a reaction-diffusion equation without uniqueness of the Cauchy problem is bounded in suitable Lr-spaces. In order to obtain this result we prove first that the concepts of weak and mild solutions are equivalent under an appropriate assumption.Also, when the nonlinear term of the equation satisfies a supercritical growth condition the existence of a weak attractor is established.

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>

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