Stability of radially symmetric travelling waves in reaction-diffusion equations
Roussier, Violaine1
1 Département de mathématique, Université de Paris-Sud, bât 425, 91405 Orsay cedex, France
Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004) no. 3, pp. 341-379.
DOI : 10.1016/j.anihpc.2003.04.002
Classification : 35B40, 35K57, 35B35
Mots-clés : Semilinear parabolic equation, Long-time asymptotics, Stability, Travelling waves
Roussier, Violaine 1

1 Département de mathématique, Université de Paris-Sud, bât 425, 91405 Orsay cedex, France 
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Roussier, Violaine. Stability of radially symmetric travelling waves in reaction-diffusion equations. Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004) no. 3, pp. 341-379. doi : 10.1016/j.anihpc.2003.04.002. http://archive.numdam.org/articles/10.1016/j.anihpc.2003.04.002/

[1] Aronson D.G., Weinberger H.F., Nonlinear diffusion in population genetics, combustion, and nerve propagation, in: Partial Differential Equations and Related Topics, Lecture Notes in Math., vol. 446, Springer, New York, 1975, pp. 5-49. | MR | Zbl

[2] Aronson D.G., Weinberger H.F., Multidimensional nonlinear diffusion arising in population genetics, Adv. Math. 30 (1978) 33-76. | MR | Zbl

[3] Fife P.C., Long time behaviour of solutions of bistable nonlinear diffusion equations, Arch. Rational Mech. Anal. 70 (1979) 31-46. | MR | Zbl

[4] Fife P.C., Mcleod J.B., The approach of solutions of nonlinear diffusion equations to travelling front solutions, Arch. Rational Mech. Anal. 65 (1977) 335-361. | MR | Zbl

[5] Fisher R.A., The advance of advantageous genes, Ann. of Eugenics 7 (1937) 355-369. | JFM

[6] Henry D., Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math., vol. 840, Springer-Verlag, New York, 1981. | MR | Zbl

[7] Jones C.K.R.T., Spherically symmetric solutions of a reaction-diffusion equation, J. Differential Equations 49 (1983) 142-169. | MR | Zbl

[8] Jones C.K.R.T., Asymptotic behaviour of a reaction-diffusion equation in higher space dimensions, Rocky Mountain J. Math. 13 (1983) 355-364. | MR | Zbl

[9] Kanel' Ya.I., On the stability of solutions of the cauchy problem for equations arising in the theory of combustion, Mat. Sb. 59 (1962) 245-288. | MR

[10] Kapitula T., Multidimensional stability of planar travelling waves, Trans. Amer. Math. Soc. 349 (1997) 257-269. | MR | Zbl

[11] Kolmogorov A.N., Petrovskii I.G., Piskunov N.S., A study of the equation of diffusion with increase in the quantity of matter, and its application to a biological problem, Bull. Moskovsk. Gos. Univ. 1 (7) (1937) 1-26.

[12] Levermore C.D., Xin J.X., Multidimensional stability of travelling waves in a bistable reaction-diffusion equation II, Comm. Partial Differential Equations 17 (1992) 1901-1924. | MR | Zbl

[13] Pazy A., Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983. | MR | Zbl

[14] Sattinger D.H., Weighted norms for the stability of travelling waves, J. Differential Equations 25 (1977) 130-144. | MR | Zbl

[15] Taylor A.E., Introduction to Functional Analysis, Wiley, New York, 1961. | MR | Zbl

[16] Uchiyama K., Asymptotic behaviour of solutions of reaction-diffusion equations with varying drift coefficients, Arch. Rational Mech. Anal. 90 (1983) 291-311. | MR | Zbl

[17] Xin J.X., Multidimensional stability of travelling waves in a bistable reaction-diffusion equation I, Comm. Partial Differential Equations 17 (1992) 1889-1899. | MR | Zbl

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