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Existence of traveling wave fronts in delayed reaction-diffusion systems via the monotone iteration method
Author(s):
Xingfu
Zou;
Jianhong
Wu
Journal:
Proc. Amer. Math. Soc.
125
(1997),
2589-2598.
MSC (1991):
Primary 34K10, 35K10, 35K55
MathSciNet review:
1415345
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Abstract:
The monotone iteration method is employed to establish the existence of traveling wave fronts in delayed reaction-diffusion systems with monostable nonlinearities.
References:
- 1.
- S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, Part I and Part II, Comm. Pure Appl. Math. 12 (1959), 623-727 and 27 (1964), 35-59. MR 23:A2610; MR 28:5252
- 2.
- N. F. Britton, Reaction-Diffusion Equations and Their Applications to Biology, Academic, New York, 1986. MR 88k:92001
- 3.
- P. C. Fife, Mathematical Aspects of Reaction-Diffusing Systems, Lecture Notes in Biomath., Vol. 28, Springer-Verlag, New York, 1979. MR 80g:35001
- 4.
- R. Gardner, Review on Traveling Wave Solutions of Parabolic Systems by Aizik I. Volpert, Vitaly A. Volpert and Vladimir A. Volpert, Bull. Amer. Math. Soc. 32 (1995), 446-452.
- 5.
- A. W. Leung, Systems of Nonlinear Partial Differential Equations with Applications to Biology and Engineering, Kluwer, Dordrecht, 1989.
- 6.
- J. D. Murray, Mathematical Biology, Springer-Verlag, New York, 1989. MR 90g:92001
- 7.
- C. V. Pao, Nonlinear Parabolic and Elliptic Equations, Plenum, New York, 1992. MR 94c:35002
- 8.
- K. W. Schaaf, Asymptotic behavior and traveling wave solutions for parabolic functional differential equations, Trans. Amer. Soc. 302 (1987), 587-615. MR 88g:35190
- 9.
- A. I. Volpert, V. A. Volpert and V. A. Volpert, Traveling Wave Solutions of Parabolic Systems, Transl. Math. Monographs, Vol. 140, Amer. Math. Soc., Providence, RI, 1994. MR 96c:35092
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Additional Information:
Xingfu
Zou
Affiliation:
Department of Mathematics and Statistics, York University, North York, Ontario, Canada M3J 1P3
Address at time of publication:
Department of Mathematics and Statistics, University of Victoria, British Columbia, Canada V8W 3P4
Email:
xzou@mathstat.yorku.ca, xzou@math.uvic.ca
Jianhong
Wu
Affiliation:
Department of Mathematics and Statistics, York University, North York, Ontario, Canada M3J 1P3
Email:
wujh@mathstat.yorku.ca
DOI:
10.1090/S0002-9939-97-04080-X
PII:
S 0002-9939(97)04080-X
Keywords:
Reaction-diffusion equations,
traveling wave fronts,
monotone iteration
Received by editor(s):
January 24, 1996
Additional Notes:
This research was partially supported by the Natural Sciences and Engineering Research Council of Canada
Communicated by:
Hal L. Smith
Copyright of article:
Copyright
1997,
American Mathematical Society
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