Abstract
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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Acknowledgements
The authors express their thanks to T. Senba for many stimulating discussions.
Anna Zhigun is sponsored by The Elite Network of Bavaria.
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Efendiev, M., Zhigun, A. (2013). On a Global Uniform Pullback Attractor of a Class of PDEs with Degenerate Diffusion and Chemotaxis in One Dimension. In: Johann, A., Kruse, HP., Rupp, F., Schmitz, S. (eds) Recent Trends in Dynamical Systems. Springer Proceedings in Mathematics & Statistics, vol 35. Springer, Basel. https://doi.org/10.1007/978-3-0348-0451-6_9
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