Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

Full text of review: PDF This review is available free of charge.

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$129.00$

*Diffusion mathematics in medicine and biology*, Bull. Inst. Math. Appl.

**12**(1976), no. 4, 106–112. MR

**681536**

*The mathematics of diffusion*, 2nd ed., Clarendon Press, Oxford, 1975. MR

**0359551**

*Reinforced random walk*, Probab. Theory Related Fields

**84**(1990), no. 2, 203–229. MR

**1030727**, DOI 10.1007/BF01197845

*Mathematical models in biology*, The Random House/Birkhäuser Mathematics Series, Random House, Inc., New York, 1988. MR

**1010228**

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

*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 10.1090/S0002-9947-1992-1046835-6

*Singularity formation in chemotaxis—a conjecture of Nagai*, SIAM J. Appl. Math.

**65**(2004), no. 1, 336–360. MR

**2112401**, DOI 10.1137/S0036139903431725

*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 10.1137/S0036139995291106

*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 10.1016/j.na.2003.11.014

*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 10.1137/S0036139995288976

*Chemotactic collapse in a parabolic-elliptic system of mathematical biology*, Adv. Differential Equations

**6**(2001), no. 1, 21–50. MR

**1799679**

*Mass normalization of collapses in the theory of self-interacting particles*, Adv. Math. Sci. Appl.

**13**(2003), no. 2, 611–623. MR

**2029934**

*Chemical Thermodynamics*, Freeman, 1958.

*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 10.1137/S0036141000337796

*The solvability of some chemotaxis systems*, J. Differential Equations

**212**(2005), no. 2, 432–451. MR

**2129098**, DOI 10.1016/j.jde.2005.01.002

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.