Abstract
AbstractThis 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 urn:x-wiley:0025584X:media:mana201700270:mana201700270-math-0001to that for the parabolic‐elliptic chemotaxis system urn:x-wiley:0025584X:media:mana201700270:mana201700270-math-0002where Ω is a bounded domain in () with smooth boundary, is a constant and χ is a function generalizing urn:x-wiley:0025584X:media:mana201700270:mana201700270-math-0006In 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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