|
Book Review
The AMS does not provide abstracts of book reviews.
You may download the entire review from the links below.
Retrieve article in:
PDF
Book Information
Author(s):
Aizik I. Volpert, Vitaly A. Volpert, and Vladimir A. Volpert
Title:
Traveling wave solutions of parabolic systems
Additional book information:
Transl. Math. Monographs, vol. 140, Amer. Math. Soc., Providence, RI, 1994, xii + 448 pp., US$142.00. ISBN 0-8218-4609-4
References:
- [1]
- J.~Alexander, R.~Gardner, and C.K.R.T. Jones, A topological invariant arising in the stability analysis of travelling waves, J. Reine Angew. Math. \textbf{410} (1990), 167--212.
- [2]
- H.~Berestycki, B.~Larrouturou, and P.~L. Lions, Multi-dimensional travelling wave solutions of a flame propagation model, Arch. Rational Mech. Anal. \textbf{111} (1990), 33--49.
- [3]
- C.~C. Conley, \emph{Isolated invariant sets and the generalized Morse index}, Amer. Math. Soc., Providence, RI, 1978.
- [4]
- J. Evans, Nerve axon equations {\rm iii:} Stability of the nerve impulses, Indiana Univ. Math. J. \textbf{22} (1972), 577--594.
- [5]
- N.~Fenichel, Persistence and smoothness of invariant manifolds for flows, Indiana Univ. Math. J. \textbf{21} (1971), 193--226.
- [6]
- P.~Fife, Asymptotic states for equations of reaction and diffusion, Bull. Amer. Math. Soc. \textbf{84} (1978), 693--726.
- [7]
- P.~Fife and J.~B. McLeod, The approach of solutions of nonlinear diffusion equations to travelling front solutions, Arch. Rational Mech. Anal. \textbf{65} (1977), 335--361.
- [8]
- P.~C. Fife, \emph{Dynamics of internal layers and diffusive interfaces}, SIAM, Philadelphia, PA, 1988.
- [9]
- R.~A. Fisher, The wave of advance of advantageous genes, Ann. Eugenics \textbf{7} (1937), 355--569.
- [10]
- R.~A. Gardner and C.K.R.T. Jones, Stability of travelling waves of diffusive predator prey systems, Trans. Amer. Math. Soc. \textbf{327} (1991), 465--524.
- [11]
- S.~Hastings, On the existence of homoclinic and periodic orbits for the Fitzhugh-Ngumo equations, Quart. J. Math. Oxford Ser. (2) \textbf{27} (1976), 123--134.
- [12]
- D.~Henry, \emph{Geometric theory of semilinear parabolic equations}, Springer, New York, 1981.
- [13]
- C.K.R.T. Jones, Stability of the traveling wave solution of the Fitzhugh-Nagumo system, Trans. Amer. Math. Soc. \textbf{286} (1984), 431--469.
- [14]
- C.K.R.T. Jones and N.~Kopell, Tracking invariant manifolds with differential forms, J. Differential Equations \textbf{108} (1994), 64--88.
- [15]
- T.~Kapitula, On the weighted stability of travelling waves in weighted $l^{\infty }$ spaces, J. Differential Equations \textbf{112} (1994), 179--215.
- [16]
- H.~Kokubu, Y.~Nishiura, and H.~Oka, Heteroclinic and homoclinic bifurcations in bistable reaction-diffusion systems, J. Differential Equations \textbf{86} (1990), 260--341.
- [17]
- A.~N. Komolgorov, I.~G. Petrovskii, and N.~S. Piskunov, Etude de l{\rm '}equation de la chaleur avec croissance de la quantite de matiere et son application a un probleme biologique, Bull. Moscov. Gos. Univ. Mat. Mekh. \textbf{1} (1937), 1--25.
- [18]
- T.-P. Liu, Nonlinear stability of shock waves for viscous conservation laws, Mem. Amer. Math. Soc. \textbf{328} (1985).
- [19]
- C.~McCord and K.~Mishaikow, Connected simple systems, transition matrices, and heteroclinic bifurcations, Trans. Amer. Math. Soc. \textbf{333} (1992), 397--422.
- [20]
- K.~Mishaikow and V.~Hutson, Travelling waves for mutualist species, SIAM J. Math. Anal. \textbf{24} (1993), 987--1008.
- [21]
- Y.~Nishiura and H.~Fujii, Stability of singularly perturbed solutions of reaction-diffusion equations, SIAM J. Math. Anal. \textbf{18} (1987), 1726--1770.
- [22]
- R.~Pego and M.~Weinstein, A class of eigenvalue problems, with applications to instability of solitary waves, Philos. Trans. Roy. Soc. London Ser. A \textbf{340} (1991), 47--94.
- [23]
- D.~Sattinger, On the stability of waves of nonlinear parabolic systems, Adv. Math. \textbf{22} (1976), 312--355.
- [24]
- J. Smoller, Shock waves and reaction-diffusion equations, Springer-Verlag, Berlin and New York, 1982.
- [25]
- A.~I. Volpert and V.~A. Volpert, Applications of the rotation theory of vector fields to the study of wave solutions of parabolic equations, Trans. Moscow Math. Soc. \textbf{52} (1990), 59--108.
- [26]
- V.~A. Volpert and A.~I. Volpert, \emph{Existence and stability of travelling waves in chemical kinetics}, ``Nauka'', Novosibirsk, 1989 pp.~56--131.
- [27]
- E.~Yanagida, Stability of the fast travelling pulse solution of the Fitzhugh-Nagumo equations, J. Math. Biol. \textbf{22} (1985), 1158--1173.
Additional Information:
Reviewer(s):
Robert
Gardner
Review Information:
Journal:
Bull. Amer. Math. Soc.
32
(1995),
446-452.
DOI:
10.1090/S0273-0979-1995-00607-5
PII:
S 0273-0979(1995)00607-5
|
Comments: webmaster@ams.org