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Efendiyev, M.A. ; Zhigun, A.*

On a global uniform pullback attractor of a class of PDEs with degenerate diffusion and chemotaxis in one dimension.

In: Recent Trends in Dynamical Systems. Heidelberg: Springer, 2013. 179-203 (Springer Proceedings in Mathematics & Statistics ; 18)
In this chapter, we deal with a class of nonautonomous degenerate parabolic systems that encompasses two different effects: porous medium and chemotaxis. Such classes of equations arise in the mesoscale level modeling of biomass spreading mechanisms via chemotaxis. Under certain "balance" conditions on the order of the porous medium degeneracy and the growth of the chemotactic function, we establish the existence of a strong uniform pull back attractor for the case of one spatial dimension, thus improving our previous study, where a weak attractor was constructed.
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Publikationstyp Artikel: Sammelbandbeitrag/Buchkapitel
Schlagwörter Attractor; Biofilms; Chemotaxis; Dissipative estimate; Nonautonomous equation; Porous-medium
ISBN 978-3-0348-0451-6
Bandtitel Recent Trends in Dynamical Systems
Quellenangaben Band: 18, Heft: , Seiten: 179-203 Artikelnummer: , Supplement: ,
Reihe Springer Proceedings in Mathematics & Statistics
Verlag Springer
Verlagsort Heidelberg