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- W2767472023 abstract "This paper gives a first 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 $$ (u_lambda)_t = Delta u_lambda - nabla cdot (u_lambda chi(v_lambda)nabla u_lambda), quad lambda (v_lambda)_t = Delta v_lambda - v_lambda +u_lambda quad mbox{in} Omegatimes (0,infty) $$ to that for the parabolic-elliptic chemotaxis system $$ u_t = Delta u -nabla cdot (uchi(v)nabla v), quad 0= Delta v -v +u quad mbox{in} Omegatimes (0,infty), $$ where $Omega$ is a bounded domain in $mathbb{R}^n$ ($ninmathbb{N}$) with smooth boundary, $lambda>0$ is a constant and $chi$ is a function generalizing $$ chi(v) = frac{chi_0}{(1+v)^k} quad (chi_0>0, k>1).$$ In chemotaxis systems parabolic-elliptic systems often provided 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. Namely, 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 $lambda searrow 0$? This paper gives some positive answer in the chemotaxis system with strong signal sensitivity." @default.
- W2767472023 created "2017-11-17" @default.
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- W2767472023 date "2017-11-05" @default.
- W2767472023 modified "2023-09-25" @default.
- W2767472023 title "The fast signal diffusion limit in a chemotaxis system with strong signal sensitivity" @default.
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