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Dimension estimate of the global attractor for a semi-discretized chemotaxis-growth system by conservative upwind finite-element scheme. (English) Zbl 1172.92311
Summary: We continue our systematic study of the dimension estimate of the global attractors for chemotaxis-growth systems and their finite-element approximations [see Discrete Contin. Dyn. Syst. 2007, Suppl., 334--343 (2007; Zbl 1163.37396)]. Utilizing a conservative upwind finite-element scheme we managed significantly to improve dimension estimates with respect to the chemotactic parameter.

MSC:
92C17Cell movement (chemotaxis, etc.)
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
37N25Dynamical systems in biology
35Q80Applications of PDE in areas other than physics (MSC2000)
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References:
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