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

Author

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  • Weijun Xie
  • Yinghui Zhang
  • Yuandong Xiao
  • Wei Wei

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 -norm of the initial perturbation around a constant state is sufficiently small. Moreover, if additionally, -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.

Suggested Citation

  • Weijun Xie & Yinghui Zhang & Yuandong Xiao & Wei Wei, 2013. "Global Existence and Convergence Rates for the Strong Solutions in to the 3D Chemotaxis Model," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-9, December.
    • Handle: RePEc:hin:jnljam:391056
    DOI: 10.1155/2013/391056
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