Pullback attractors of nonautonomous reaction–diffusion equations
By Haitao Song, Hongqing Wu. 2007
71 citations recorded by the source corpus.
Abstract In this paper, firstly we introduce the concept of norm-to-weak continuous cocycle in Banach space and give a technical method to verify this kind of continuity, then we obtain some abstract results for the existence of pullback attractors about this kind of cocycle, using the measure of noncompactness. As an application, we prove the existence of pullback attractors in H 0 1 of the cocycle associated with the solutions for some nonlinear nonautonomous reaction–diffusion equations. The attractor pullback attracts all bounded subsets of H 0 1 in the norm of H 0 1 .
Subfields: Computational Theory and Mathematics, Computer Networks and Communications, Control and Systems Engineering
View Paper: https://www.semanticscholar.org/paper/a6e4197c4d11a72a17ac9a7259911bc6e478f2f5
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Theory and Mathematics
In Computer Networks and Communications
In Control and Systems Engineering
Citations in the corpus
- Pullback attractors for a class of non-autonomous nonclassical diffusion equations (2010, background): “1) in the case ε = 0 has been studied in [11–14].”
- On the existence of pullback attractors for non-autonomous reaction–diffusion equations (2008, unknown): “As for our problems, recently, in [16], the authors studied the pullback asymptotic behaviour of the solutoins of equation (1.”