具有间接信号产生和表型转换功能的趋化模型的奇异极限

IF 1.6 2区 数学 Q2 MATHEMATICS, APPLIED Nonlinearity Pub Date : 2024-09-03 DOI:10.1088/1361-6544/ad6bdf
Philippe Laurençot, Christian Stinner
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引用次数: 0

摘要

在二维环境中,当切换率增加到无穷大时,显示了具有间接信号产生和表型切换的部分扩散趋化系统解的收敛性,从而为文献中的正式计算提供了严格的证明。预期的极限系统是经典的抛物线-抛物线凯勒-西格尔系统,对于一般初始条件,所获得的收敛性被限制在有限的时间间隔内,但当初始条件的质量适当小时,收敛性对任意有界时间间隔有效。此外,如果极限系统的解在有限时间内炸毁,那么部分扩散系统中的两个表型在该时间之后都不能均匀地受 L2 规范约束。
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Singular limit of a chemotaxis model with indirect signal production and phenotype switching
Convergence of solutions to a partially diffusive chemotaxis system with indirect signal production and phenotype switching is shown in a two-dimensional setting when the switching rate increases to infinity, thereby providing a rigorous justification of formal computations performed in the literature. The expected limit system being the classical parabolic–parabolic Keller–Segel system, the obtained convergence is restricted to a finite time interval for general initial conditions but valid for arbitrary bounded time intervals when the mass of the initial condition is appropriately small. Furthermore, if the solution to the limit system blows up in finite time, then neither of the two phenotypes in the partially diffusive system can be uniformly bounded with respect to the L2-norm beyond that time.
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来源期刊
Nonlinearity
Nonlinearity 物理-物理:数学物理
CiteScore
3.00
自引率
5.90%
发文量
170
审稿时长
12 months
期刊介绍: Aimed primarily at mathematicians and physicists interested in research on nonlinear phenomena, the journal''s coverage ranges from proofs of important theorems to papers presenting ideas, conjectures and numerical or physical experiments of significant physical and mathematical interest. Subject coverage: The journal publishes papers on nonlinear mathematics, mathematical physics, experimental physics, theoretical physics and other areas in the sciences where nonlinear phenomena are of fundamental importance. A more detailed indication is given by the subject interests of the Editorial Board members, which are listed in every issue of the journal. Due to the broad scope of Nonlinearity, and in order to make all papers published in the journal accessible to its wide readership, authors are required to provide sufficient introductory material in their paper. This material should contain enough detail and background information to place their research into context and to make it understandable to scientists working on nonlinear phenomena. Nonlinearity is a journal of the Institute of Physics and the London Mathematical Society.
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