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

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


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