The fast signal diffusion limit in a chemotaxis system with strong signal sensitivity |
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Authors: | Masaaki Mizukami |
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Institution: | 1. Department of Mathematics, Tokyo University of Science, 1‐3, Kagurazaka, Shinjuku‐ku, Tokyo, 162‐8601 Japan;2. Dr. Masaaki Mizukami, Department of Mathematics, Tokyo University of Science, 1‐3, Kagurazaka, Shinjuku‐ku, Tokyo 162‐8601, Japan. |
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Abstract: | This paper gives an insight into making a mathematical bridge between the parabolic‐parabolic signal‐dependent chemotaxis system and its parabolic‐elliptic version. To be more precise, this paper deals with convergence of a solution for the parabolic‐parabolic chemotaxis system with strong signal sensitivity to that for the parabolic‐elliptic chemotaxis system where Ω is a bounded domain in () with smooth boundary, is a constant and χ is a function generalizing In chemotaxis systems parabolic‐elliptic systems often gave some guide to methods and results for parabolic‐parabolic systems. However, the relation between parabolic‐elliptic systems and parabolic‐parabolic systems has not been studied except for the case that . Namely, in the case that Ω is a bounded domain, it still remains to analyze on the following question: Does a solution of the parabolic‐parabolic system converge to that of the parabolic‐elliptic system as ? This paper gives some positive answer in the chemotaxis system with strong signal sensitivity. |
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Keywords: | chemotaxis system with signal sensitivity parabolic‐parabolic system parabolic‐elliptic system Primary: 35A09 Secondary: 35J15 35K51 92C17 |
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