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$129.00$
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 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, Erratum to: Singularity formation in chemotaxis - a conjecture of Nagai, SIAM J. Appl. Math. (in press).
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 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 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 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 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 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, Chemical Thermodynamics, Freeman, 1958.
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 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 10.1016/j.jde.2005.01.002
crank1 J. Crank, Diffusion mathematics in medicine and biology, Bull. Inst. Math. Appl., 12 (1976), pp. 106–112.
crank —, The Mathematics of Diffusion, Clarendon Press, Oxford, 2 ed., 1975.
D B. Davis, Reinforced random walks, Prob. Theory Related Fields, 84 (1990), pp. 203–229.
MR1010228 L. Edelstein-Keshet, Mathematical models in biology, The Random House/Birkhäuser Mathematics Series, Random House Inc., New York, 1988.
HLR M. A. Halverson, H. A. Levine, and J. Rencławowicz, Erratum to: Singularity formation in chemotaxis - a conjecture of Nagai, SIAM J. Appl. Math. (in press).
Jagl W. Jäger and S. Luckhaus, On explosions of solutions to a system of partial differential equations modelling chemotaxis, Trans. Amer. Math. Soc., 329 (1992), pp. 819–824.
LR2 H. A. Levine and J. Rencławowicz, Singularity formation in chemotaxis—a conjecture of Nagai, SIAM J. Appl. Math., 65 (2004), pp. 336–360 (electronic).
LS H. A. Levine and B. D. Sleeman, A system of reaction diffusion equations arising in the theory of reinforced random walks, SIAM J. Appl. Math., 57 (1997), pp. 683–730.
Nag1 T. Nagai and T. Nakaki, Stability of constant steady states and existence of unbounded solutions in time to a reaction-diffusion equation modelling chemotaxis, Nonlinear Analysis, 58 (2004), pp. 657–81.
OS H. G. Othmer and A. Stevens, Aggregation, blow up and collapse: The abc’s of taxis and reinforced random walks, SIAM J. Appl. Math., 57 (1997), pp. 1044–1081.
MR1799679 T. Senba and T. Suzuki, Chemotactic collapse in a parabolic-elliptic system of mathematical biology, Adv. Differential Equations, 6 (2001), pp. 21–50.
MR2029934 T. Suzuki, Mass normalization of collapses in the theory of self-interacting particles, Adv. Math. Sci. Appl., 13 (2003), pp. 611–623.
Wall F. T. Wall, Chemical Thermodynamics, Freeman, 1958.
yang2 Y. Yang, H. Chen, and W. Liu, On existence of global solutions and blow-up to a system of reaction-diffusion equations modelling chemotaxis, SIAM J. Math. Anal., 33 (2001), pp. 763–785.
yang3 Y. Yang, C. Hua, L. Weian, and B. D. Sleeman, The solvability of some chemotaxis systems, J. Differential Equations, 212 (2005), pp. 432–451.
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.
