Global solutions and exponential attractors  of a parabolic-parabolic system    for chemotaxis  with subquadratic degradation

Etsushi Nakaguchi; Koichi Osaki

doi:10.3934/dcdsb.2013.18.2627

Article Contents

2013, Volume 18, Issue 10: 2627-2646. Doi: 10.3934/dcdsb.2013.18.2627 open access

This issue Previous Article Pattern formation of the attraction-repulsion Keller-Segel system Next Article Well-posedness for a model of individual clustering

Global solutions and exponential attractors of a parabolic-parabolic system for chemotaxis with subquadratic degradation

Etsushi Nakaguchi^1, and
Koichi Osaki^2,

1.
College of Liberal Arts and Sciences, Tokyo Medical and Dental University, 2-8-30 Kohnodai, Ichikawa, Chiba 272-0827
2.
Department of Mathematical Sciences, School of Science and Technology, Kwansei Gakuin University, 2-1 Gakuen, Sanda 669-1337

Received: November 30, 2012

Revised: June 30, 2013

Published: November 2013

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Abstract

We construct the global bounded solutions and the attractors of a parabolic-parabolic chemotaxis-growth system in two- and three-dimensional smooth bounded domains. We derive new $L_p$ and $H^2$ uniform estimates for these solutions. We then construct the absorbing sets and the global attractors for the dynamical systems generated by the solutions. We also show the existence of exponential attractors by applying the existence theorem of Eden-Foias-Nicolaenko-Temam.

Keywords:

Mathematics Subject Classification: 37L30, 35B41, 35K51, 35K57, 35K92, 92C17.

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