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.
@article{AIHPC_2004__21_3_341_0,
author = {Roussier, Violaine},
title = {Stability of radially symmetric travelling waves in reaction-diffusion equations},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {341--379},
publisher = {Elsevier},
volume = {21},
number = {3},
year = {2004},
doi = {10.1016/j.anihpc.2003.04.002},
zbl = {1066.35018},
language = {en},
url = {www.numdam.org/item/AIHPC_2004__21_3_341_0/}
}
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://www.numdam.org/item/AIHPC_2004__21_3_341_0/

[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 427837 | Zbl 0325.35050

[2] Aronson D.G., Weinberger H.F., Multidimensional nonlinear diffusion arising in population genetics, Adv. Math. 30 (1978) 33-76. | MR 511740 | Zbl 0407.92014

[3] Fife P.C., Long time behaviour of solutions of bistable nonlinear diffusion equations, Arch. Rational Mech. Anal. 70 (1979) 31-46. | MR 535630 | Zbl 0435.35045

[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 442480 | Zbl 0361.35035

[5] Fisher R.A., The advance of advantageous genes, Ann. of Eugenics 7 (1937) 355-369. | JFM 63.1111.04

[6] Henry D., Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math., vol. 840, Springer-Verlag, New York, 1981. | MR 610244 | Zbl 0456.35001

[7] Jones C.K.R.T., Spherically symmetric solutions of a reaction-diffusion equation, J. Differential Equations 49 (1983) 142-169. | MR 704268 | Zbl 0523.35059

[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 702830 | Zbl 0528.35054

[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 157130

[10] Kapitula T., Multidimensional stability of planar travelling waves, Trans. Amer. Math. Soc. 349 (1997) 257-269. | MR 1360225 | Zbl 0866.35021

[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 1194744 | Zbl 0789.35020

[13] Pazy A., Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983. | MR 710486 | Zbl 0516.47023

[14] Sattinger D.H., Weighted norms for the stability of travelling waves, J. Differential Equations 25 (1977) 130-144. | MR 447813 | Zbl 0315.35010

[15] Taylor A.E., Introduction to Functional Analysis, Wiley, New York, 1961. | MR 98966 | Zbl 0081.10202

[16] Uchiyama K., Asymptotic behaviour of solutions of reaction-diffusion equations with varying drift coefficients, Arch. Rational Mech. Anal. 90 (1983) 291-311. | MR 801583 | Zbl 0618.35058

[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 1194743 | Zbl 0789.35019