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The Basin of Attraction of the Steady-States for a Chemotaxis Model in \({\mathbb{R}^2}\) with Critical Mass

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Abstract

We consider the Cauchy problem for a parabolic–elliptic system in \({\mathbb{R}^2}\), which is amathematical model of chemotaxis and also amodel of self-attracting particles. In the critical mass case, we determine the basin of attraction of the steady-states for the Cauchy problem through a Lyapunov functional.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040, Madrid, Spain

    Julián López-Gómez

  2. Department of Mathematics, Graduate School of Science, Hiroshima University, Higashi-Hiroshima, 739-8526, Japan

    Toshitaka Nagai & Tetsuya Yamada

Authors
  1. Julián López-Gómez
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  2. Toshitaka Nagai
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  3. Tetsuya Yamada
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Corresponding author

Correspondence to Julián López-Gómez.

Additional information

Communicated by P. H. Rabinowitz

The research of J. López-Gómez and T. Nagai has been supported by the Spanish Ministry of Science and Technology under Grants MTM2009-08259 and MTM2012-30669.

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López-Gómez, J., Nagai, T. & Yamada, T. The Basin of Attraction of the Steady-States for a Chemotaxis Model in \({\mathbb{R}^2}\) with Critical Mass. Arch Rational Mech Anal 207, 159–184 (2013). https://doi.org/10.1007/s00205-012-0560-1

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  • DOI: https://doi.org/10.1007/s00205-012-0560-1

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