Speed of fronts of generalized reaction-diffusion equations

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 57, Issue 6, 1998, Pages 6493-6496

  Benguria, R D ^a   Depassier, M C ^a  

^a PONTIFICIA UNIVERSIDAD CATÓLICA DE CHILE   (Chile)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001059738     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.57.6493     Document Type: Article

References (13)

1. D. G. Aronson and H. F. Weinberger, Adv. Math. 30, 33 (1978).ADMTA4
2. A. N. Kolmogorov, I. G. Petrovskii, and N. S. Piskunov, in Selected Works of A. N. Kolmogorov edited by V. M. Tikhomirov (Kluwer Academic, Amsterdam, 1991).
3. G. Dee and J. S. Langer, Phys. Rev. Lett. 50, 383 (1983).PRLTAO
4. K. P. Kadeler and F. Rothe, J. Math. Biol. 2, 251 (1975).JMBLAJ
5. R. D. Benguria and M. C. Depassier, Commun. Math. Phys. 175, 221 (1996).CMPHAY
6. R. D. Benguria and M. C. Depassier, Phys. Rev. Lett. 77, 1171 (1996).PRLTAO
7. A. I. Volpert, V. A. Volpert, and V. A. Volpert, Traveling Wave Solutions of Parabolic Systems, Translations of Mathematical Monographs Vol. 140 (American Mathematical Society, Providence, RI, 1994).
8. Y. Cherniak, Phys. Rev. E 56, 2061 (1997).PLEEE8
9. D. H. Sattinger, Adv. Math. 22, 312 (1976).ADMTA4
10. T. Kapitula, J. Diff. Eqns. 112, 179 (1994).JDEQAK
11. X. Y. Wang, S. Fan, and T. Kyu, Phys. Rev. E 56, R4931 (1997).PLEEE8
12. R. D. Benguria and M. C. Depassier, Phys. Rev. Lett. 73, 2272 (1994).PRLTAO
13. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 5th ed. (Academic Press, San Diego, 1994). See p. 1133 of this edition, formula HL151. The inequality is given for convex functions φ. If φ is a convex function, then -φ is concave and the inequality for -φ holds with the sign reversed. Take the function -φ to be the square root.