On asymptotic behaviors of solutions to parabolic systems modelling chemotaxis |
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| Authors: | Yoshiyuki Kagei Yasunori Maekawa |
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| Institution: | 1. Faculty of Mathematics, Kyushu University, Motooka 744, Nishi-ku, Fukuoka, 819-0395, Japan;2. Department of Mathematics, Graduate School of Science, Kobe University, 1-1, Rokkodai, Nada-ku, Kobe, 657-8501, Japan |
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| Abstract: | This paper deals with large time behaviors of solutions to a Keller–Segel system which possesses self-similar solutions. By taking into account the invariant properties of the equation with respect to a scaling and translations, we show that suitably shifted self-similar solutions give more precise asymptotic profiles of general solutions at large time. The convergence rate is also computed in details. |
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