Global Existence and Convergence Rates for the Strong Solutions in H2 to the 3D Chemotaxis Model

Weijun Xie, Yinghui Zhang, Yuandong Xiao and Wei Wei

Journal of Applied Mathematics, 2013, vol. 2013, issue 1

Abstract: We are concerned with a 3D chemotaxis model arising from biology, which is a coupled hyperbolic‐parabolic system. We prove the global existence of a strong solution when H2‐norm of the initial perturbation around a constant state is sufficiently small. Moreover, if additionally, L1‐norm of the initial perturbation is bounded; the optimal convergence rates are also obtained for such a solution. The proofs are obtained by combining spectral analysis with energy methods.

Date: 2013
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https://doi.org/10.1155/2013/391056

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2013:y:2013:i:1:n:391056

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