Abstract
We propose an approximate method to obtain the speed of wavefronts. It is built up from a known variational principle. For a range of systems of biological and physical interest, comparison to previously-known solutions and to numerical simulations shows the powerfulness of our approximate technique. For time-delayed equations, we also propose an alternative approximate solution, based on the renormalization group approach, and we compare both approximations.
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REFERENCES
J. Fort, T. Pujol, and A. S. Cukrowski, J. Phys. A: Math. Gen. 33:6953 (2000).
V. Méndez, Phys. Rev. E 57:3622 (1998).
J. Fort and V. Méndez, Phys. Rev. Lett. 82:867 (1999); Phys. Rev. E 60:5894 (1999).
R. Benguria and M. C. Depassier, Phys. Rev. Lett. 73:2272 (1994); Phys. Rev. E. 52:3258 (1995); 57:6493 (1998).
M. A. Livshits, G. T. Gurija, B. N. Belinstev, and M. V. Volkenstein, J. Math. Biol. 11:295 (1981).
E. Ben-Jacob, H. Brand, G. Dee, L. Kramer, and J. S. Langer, Physica D 14:348 (1985).
I. S. Gradshteyn and I. M. Ryzik, Table of Integrals, Series, and Products (Academic Press, Boston, 1994).
H. M. Lieberstein, Math. Biosci. 1:45 (1967); H. P. McKean, Adv. Math. 4:209 (1970).
K. P. Hadeler and F. Rothe, J. Math. Biol. 2:251 (1975).
J. D. Murray, Mathematical Biology, 2nd ed. (Springer, New York, 1993).
S. J. Di Bartolo and A. T. Dorsey, Phys. Rev. Lett. 77:4442 (1996).
D. A. Kessler, Z. Ner, and L. M. Sander, Phys. Rev. E 58:107 (1998).
E. Magyari, J. Phys. A 15:L139 (1982).
V. Méndez and J. E. Llebot, Phys. Rev. E 56:6557 (1997).
V. Méndez, J. Fort, and J. Farjas, Phys. Rev. E 60:5231 (1999).
Reference 15 (the case considered in this section corresponds to a=0 in that reference, Section 4.4).
K. M. Vereecken, E. J. Dens, and J. F. Van Impe, J. Theor. Biol. 205:53 (2000).
V. Méndez and J. Camacho, Phys. Rev. E 55:6476 (1997).
G. Dee and J. S. Langer, Phys. Rev. Lett. 50:383 (1983).
G. C. Paquette, L-Y. Chen, N. Goldenfeld, and Y. Oono, Phys. Rev. Lett. 72:76 (1994); L.-Y. Chen, N. Goldenfeld, and Y. Oono, Phys. Rev. E 49:4502 (1994).
V. Méndez and J. Fort, Phys. Rev. E 64:011105 (2001).
See Eq. (11) and Sections 4.1 and 4.2 in ref. 15. See also ref. 3.
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Fort, J., Méndez, V. On Approximate Solutions to the Wavefront Speed Problem. Journal of Statistical Physics 107, 805–820 (2002). https://doi.org/10.1023/A:1014590230955
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DOI: https://doi.org/10.1023/A:1014590230955