趋化运动双曲模型弱解的存在唯一性

王剑苹, 吴少华

数学学报 ›› 2015, Vol. 58 ›› Issue (6) : 993-1000.

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数学学报 ›› 2015, Vol. 58 ›› Issue (6) : 993-1000. DOI: 10.12386/A2015sxxb0098
论文

趋化运动双曲模型弱解的存在唯一性

    王剑苹, 吴少华
作者信息 +

Existence and Uniqueness of Weak Solutions for a Hyperbolic Chemotaxis Model

    Jian Ping WANG, Shao Hua WU
Author information +
文章历史 +

摘要

研究了一维空间上趋化运动的一个双曲模型,相对于传统的描述微粒群整体运动的Goldstein--Kac模型,我们提出的模型则描述单个微粒的运动. 在假设微生物的运动速度是常数,并且s的生产和消退是线性的基础上, 得到了弱解的局部存在唯一性.

Abstract

We study a hyperbolic model for chemotaxis in one space dimension. Comparing with the generalized Goldstein–Kac model which describes the movement of total population, the model we present here explains the movement of each particle. We assume the speed and turning rates are constant, and the reproduction and degradation of s is linear. Local existence and uniqueness for weak solutions are shown.

关键词

趋化作用 / 双曲模型 / 弱解

Key words

chemotaxis / hyperbolic model / weak solutions

引用本文

导出引用
王剑苹, 吴少华. 趋化运动双曲模型弱解的存在唯一性. 数学学报, 2015, 58(6): 993-1000 https://doi.org/10.12386/A2015sxxb0098
Jian Ping WANG, Shao Hua WU. Existence and Uniqueness of Weak Solutions for a Hyperbolic Chemotaxis Model. Acta Mathematica Sinica, Chinese Series, 2015, 58(6): 993-1000 https://doi.org/10.12386/A2015sxxb0098

参考文献

[1] Alt W., Biased random walk model for chemotaxis and related diffusion approximation, J. Math. Biol., 1980, 9: 147–177.

[2] Alt W., Singular perturbation of differential integral equations describing biased random walks, J. Reine. Angew. Math., 1981, 322: 15–41.

[3] Chen H., Wu S. H., On existence of solutions for some hyperbolic-parabolic type chemotaxis systems, IMA J. Appl. Math., 2007, 72: 331–347.

[4] Chen H., Wu S. H., The free boundary problem in biological phenomena, J. Partial Differential Equations, 2007, 20: 155–168.

[5] Chen H., Wu S. H., Hyperbolic-parabolic chemotaxis system with nonlinear product terms, J. Partial Differential Equations, 2008, 21: 45–48.

[6] Chen H., Wu S. H., The moving boundary problem in a chemotaxis model, Comm. Pure. Appl. Anal., 2012, 11(2): 735–746.

[7] Goldstein S., On diffusion by discontinuous movements and the telegraph equation, Quart. J. Mech. Appl. Math., 1951, 4: 129–156.

[8] Greenberg J. M., Alt W., Stability results for a diffusion equation with functional drift approximating a chemotaxis model, Trans. Amer. Math. Set., 1987, 300(1): 235–258.

[9] Hillen T., A Turing model with correlated random walk, J. Math. Biol., 1996, 35: 49–72.

[10] Hillen T., Invariance principles for hyperbolic random walk systems, J. Math. Anal. Appl., 1997, 210: 360– 374.

[11] Hillen T., Stevens. A., Hyperbolic models for chemotaxis in 1-D, Nonlinear Anal. Real World Appl., 2000, 1: 409–433.

[12] Keller E. F., Segel L. A., Initiation of slime mold aggregation viewed as an instability, J. Theor. Biol., 1970, 26: 399–415.

[13] Murray J. D., Mathematical Biology, Springer, New York, 1989.

[14] Soll D. R., Behavioral studies into the mechanism of eukaryotic chemotaxis, J. Chemical Ecology, 1990, 16: 133–150.

[15] Segel L. A., A theoretical study of receptor mechanisms in bacterial chemotaxis, SIAM Appl. Math, 1977, 32: 653–665.

[16] Taylor M. E., Partial Differential Equations III, Springer, New York, 1996.

[17] Wu S. H., A free boundary problem to a chemotaxis system, Acta Math. Sinica, Chinese Series, 2010, 53(3): 515–524.

[18] Wu S. H., Chen H., Nonlinear hyperbolic–parabolic system modeling some biological phenomena, J. Partial Differential Equations, 2011, 24(1): 1–14.

[19] Wu S. H., Chen. H., Li. W. X., The local and global existence of the solutions of hyperbolic-parabolic system modeling biological phenomena, Acta Math. Scientia, 2008, 28: 101–116.

[20] Wu S. H., Yue. B., On existence of local solutions of a moving boundary problem modelling chemotaxis in 1-D, J. Partial Differential Equations, 2014, 27(3): 268–282.
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