Travelling wave solutions for some models in phytopathology

Nonlinear Analysis: Real World Applications

Volumn 10, Issue 4, 2009, Pages 2307-2325

  Burie, J B ^a   Ducrot, A ^a  

^a UNIVERSITÉ BORDEAUX 1   (France)

Author keywords

Measure kernel convolution; Time delay integro differential equations; Travelling waves

Indexed keywords

CONVOLUTION; INTEGRODIFFERENTIAL EQUATIONS; NONLINEAR EQUATIONS; TIME DELAY; WAVE TRANSMISSION;

DIFFERENTIAL SYSTEMS; EXISTENCE AND UNIQUENESS; FUNGAL DISEASE; MEASURE KERNEL CONVOLUTION; NON-LINEAR INTEGRAL EQUATIONS; REACTION-DIFFUSION SYSTEMS; TIME DELAY INTEGRO-DIFFERENTIAL EQUATIONS; TRAVELLING WAVE SOLUTIONS; TRAVELLING WAVES;

ORDINARY DIFFERENTIAL EQUATIONS;

EID: 61749083969     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2008.04.013     Document Type: Article

References (18)

1. Burie J.-B., Calonnec A., and Langlais M. Modeling of the invasion of a fungal disease over a vineyard. In: Deutsch A., Bravo de la Parra R., de Boer R., Diekmann O., Jagers P., Kisdi E., Kretzschmar M., Lansky P., and Metz H. (Eds). Mathematical Modeling of Biological Systems vol. II (2007), Birkhauser, Boston 11-21
2. Chung S.-Y. Quasianalycity of positive definite continuous functions. Publ. RIMS, Kyoto univ. 38 (2002) 725-733
3. Diekmann O. Run for your life, a note on the asymptotic speed of propagation of an epidemic. J. Differential Equations 33 (1979) 58-73
4. Diekmann O., and Kaper H.G. On the bounded solutions of a nonlinear convolution equation. Nonlinear Anal. TMA 2 (1978) 721-737
5. Tufto J., Engen S., and Hindar K. Stochastic dispersal processes in plant populations. Theor. Popul. Biol. 52 (1997) 16-26
6. Fife P., and McLeod J.B. The approach of solutions of nonlinear diffusion equation to travelling front solutions. Arch. Rational Mech. Anal. 65 (1977) 335-361
7. Fisher R.A. The wave of advance of advantageous genes. Ann. Eugenics 7 (1937) 355-369
8. Gourley S.A., and Ruan S. Convergence and travelling fronts in functional differential equations with nonlocal terms: A competition model. SIAM J. Math. Anal. 35 (2003) 806-822
9. Huang J., and Zou X. Existence of travelling wavefronts of delayed reaction-diffusion systems without monotonicity. Discrete Contin. Dyn. Syst. 9 (2003) 925-936
10. Lan K., and Wu J. Travelling wavesfronts of reaction-diffusion equations with and without delays. Nonlinear Anal. RWA 4 (2003) 173-188
11. Segarra J., Seger M.J., and van den Bosch F. Epidemic dynamics and patterns of plant diseases. Phytopathology 91 (2001) 1001-1010
12. Shigesada N., and Kawasaki K. Biological invasions: Theory and practice. Oxford Series in Ecology and Evolution (1997), Oxford University Press, Oxford
13. Shigesada N., and Kawasaki K. Invasion and the range expansion of species: Effects of long-distance dispersal. In: Bullock J., Kenward R., and Hails R. (Eds). Dispersal Ecology (2002), Blackwell Science, Malden MA 350-373
14. Thieme H.R. Asymptotic estimates of the solutions of a nonlinear integral equations and asymptotic speed of spread. J. Reine Angew. Math. 306 (1979) 94-121
15. Thieme H.R. Density-dependent regulation of spatially distributed populations and their asymptotic speed of spread. J. Math. Biol. 8 (1979) 173-187
16. Thieme H.R., and Zhao X.Q. Asymptotic speeds of spread and traveling waves for integral equations and delayed reaction-diffusion models. J. Differential Equations 195 (2003) 430-470
17. Volpert A., Volpert Vit., and Volpert Vl. Traveling Wave Solutions of Parabolic Systems. Translation of Mathematical Monographs vol. 140 (1994), Amer. Math. Society, Providence
18. Zawolek M.W., and Zadoks J.C. Studies in focus development: An optimum for the dual dispersal of plant pathogens. Phytopathology 82 (1992) 1288-1297