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On a fully parabolic chemotaxis system with source term and periodic asymptotic behavior

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Abstract

We study a parabolic–parabolic chemotactic PDE’s system which describes the evolution of a biological population “u” and a chemical substance “v” in a two-dimensional bounded domain with regular boundary. We consider a growth term of logistic type in the equation of “u” in the form \(u (1-u+f(x,t))\), for a given bounded function “f” which tends to a periodic in time function independent of x when t goes to infinity. We study the global existence of solutions and its asymptotic behavior for a range of parameters and initial data.

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Acknowledgements

This work is supported by the Project MTM2017-83391-P from MICINN (Spain).

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Authors and Affiliations

  1. Depto. de Análisis Matemático y Matemática Aplicada, Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid, 28040, Madrid, Spain

    M. Negreanu

  2. Depto. Matemáticas Fundamentales. Facultad de Ciencias, Universidad Nacional de Educación a Distancia, 28040, Madrid, Spain

    J. I. Tello

  3. Universidad Complutense de Madrid, 28040, Madrid, Spain

    A. M. Vargas

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  1. M. Negreanu
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  2. J. I. Tello
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  3. A. M. Vargas
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Correspondence to J. I. Tello.

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Negreanu, M., Tello, J.I. & Vargas, A.M. On a fully parabolic chemotaxis system with source term and periodic asymptotic behavior. Z. Angew. Math. Phys. 71, 65 (2020). https://doi.org/10.1007/s00033-020-1282-0

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  • DOI: https://doi.org/10.1007/s00033-020-1282-0

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