Pullback exponential attractors for nonautonomous equations Part I: Semilinear parabolic problems

By R. Czaja, Messoud A. Efendiev. 2011

57 citations recorded by the source corpus.

A family of compact and positively invariant sets with uniformly bounded fractal dimension which at a uniform exponential rate pullback attract bounded subsets of the phase space under the process is constructed. The existence of such a family, called a pullback exponential attractor, is proved for a nonautonomous semilinear abstract parabolic Cauchy problem. Specific examples will be presented in the forthcoming Part II of this work.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6f31019cd1749e362018e0b1a5518367a911770b

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In Computational Theory and Mathematics

1. Alexandre Nolasco de Carvalho
2. Stefanie Sonner
3. Bixiang Wang
4. José M. Arrieta
5. German Lozada-Cruz

In Control and Systems Engineering

1. Stefanie Sonner
2. Alexandre Nolasco de Carvalho
3. Bixiang Wang
4. Chunyou Sun
5. José M. Arrieta
6. German Lozada-Cruz

In Mathematical Physics

1. Alexandre Nolasco de Carvalho
2. Stefanie Sonner
3. Chunyou Sun

Citations in the corpus

• Pullback exponential attractors for evolution processes in Banach spaces: Properties and applications (2013, methodology): “They consider asymptotically compact evolution processes in the weaker space W , a construction for processes that are asymptotically compact in the stronger phase space V as we formulated in [5] has not been considered before (see [8], [16], [13] and for autonomous exponential attractors [12], [11]”