Book Review

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Book Information:

Author: Takashi Suzuki

Title: Free energy and self-interacting particles

Additional book information: Birkhäuser Boston, Inc., Boston, 2005, xiv+366 pp., ISBN 0-8176-4302-8, US$129.00$

- John Crank,
*Diffusion mathematics in medicine and biology*, Bull. Inst. Math. Appl.**12**(1976), no. 4, 106–112. MR**681536** - J. Crank,
*The mathematics of diffusion*, 2nd ed., Clarendon Press, Oxford, 1975. MR**0359551** - Burgess Davis,
*Reinforced random walk*, Probab. Theory Related Fields**84**(1990), no. 2, 203–229. MR**1030727**, DOI https://doi.org/10.1007/BF01197845 - Leah Edelstein-Keshet,
*Mathematical models in biology*, The Random House/Birkhäuser Mathematics Series, Random House, Inc., New York, 1988. MR**1010228**
HLR M. A. Halverson, H. A. Levine, and J. Rencławowicz, - W. Jäger and S. Luckhaus,
*On explosions of solutions to a system of partial differential equations modelling chemotaxis*, Trans. Amer. Math. Soc.**329**(1992), no. 2, 819–824. MR**1046835**, DOI https://doi.org/10.1090/S0002-9947-1992-1046835-6 - Howard A. Levine and Joanna Rencławowicz,
*Singularity formation in chemotaxis—a conjecture of Nagai*, SIAM J. Appl. Math.**65**(2004), no. 1, 336–360. MR**2112401**, DOI https://doi.org/10.1137/S0036139903431725 - Howard A. Levine and Brian D. Sleeman,
*A system of reaction diffusion equations arising in the theory of reinforced random walks*, SIAM J. Appl. Math.**57**(1997), no. 3, 683–730. MR**1450846**, DOI https://doi.org/10.1137/S0036139995291106 - Toshitaka Nagai and Tatsuyuki Nakaki,
*Stability of constant steady states and existence of unbounded solutions in time to a reaction-diffusion equation modelling chemotaxis*, Nonlinear Anal.**58**(2004), no. 5-6, 657–681. MR**2078740**, DOI https://doi.org/10.1016/j.na.2003.11.014 - Hans G. Othmer and Angela Stevens,
*Aggregation, blowup, and collapse: the ABCs of taxis in reinforced random walks*, SIAM J. Appl. Math.**57**(1997), no. 4, 1044–1081. MR**1462051**, DOI https://doi.org/10.1137/S0036139995288976 - Takasi Senba and Takashi Suzuki,
*Chemotactic collapse in a parabolic-elliptic system of mathematical biology*, Adv. Differential Equations**6**(2001), no. 1, 21–50. MR**1799679** - Takashi Suzuki,
*Mass normalization of collapses in the theory of self-interacting particles*, Adv. Math. Sci. Appl.**13**(2003), no. 2, 611–623. MR**2029934**
Wall F. T. Wall, - Yin Yang, Hua Chen, and Weian Liu,
*On existence of global solutions and blow-up to a system of the reaction-diffusion equations modelling chemotaxis*, SIAM J. Math. Anal.**33**(2001), no. 4, 763–785. MR**1884721**, DOI https://doi.org/10.1137/S0036141000337796 - Yang Yin, Chen Hua, Liu Weian, and B. D. Sleeman,
*The solvability of some chemotaxis systems*, J. Differential Equations**212**(2005), no. 2, 432–451. MR**2129098**, DOI https://doi.org/10.1016/j.jde.2005.01.002

*Erratum to: Singularity formation in chemotaxis - a conjecture of Nagai*, SIAM J. Appl. Math. (in press).

*Chemical Thermodynamics*, Freeman, 1958.

Review Information:

Reviewer: Howard A. Levine

Affiliation: Iowa State University

Journal: Bull. Amer. Math. Soc.

**44**(2007), 139-145

Published electronically: August 2, 2006

Review copyright: © Copyright 2006 American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.