no. 3
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
Keywords: 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 
@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},
     year = {2004},
     publisher = {Elsevier},
     volume = {21},
     number = {3},
     doi = {10.1016/j.anihpc.2003.04.002},
     zbl = {1066.35018},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpc.2003.04.002/}
}
TY  - JOUR
AU  - Roussier, Violaine
TI  - Stability of radially symmetric travelling waves in reaction-diffusion equations
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2004
SP  - 341
EP  - 379
VL  - 21
IS  - 3
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.1016/j.anihpc.2003.04.002/
DO  - 10.1016/j.anihpc.2003.04.002
LA  - en
ID  - AIHPC_2004__21_3_341_0
ER  - 
%0 Journal Article
%A Roussier, Violaine
%T Stability of radially symmetric travelling waves in reaction-diffusion equations
%J Annales de l'I.H.P. Analyse non linéaire
%D 2004
%P 341-379
%V 21
%N 3
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.anihpc.2003.04.002/
%R 10.1016/j.anihpc.2003.04.002
%G en
%F 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

[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. | Zbl | MR

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

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

[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. | Zbl | MR

[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. | Zbl | MR

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

[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. | Zbl | MR

[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. | Zbl | MR

[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. | Zbl | MR

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

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

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

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

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

Cité par Sources :