Stability of radially symmetric travelling waves in reaction–diffusion equations

Violaine Roussier

Annales de l'I.H.P. Analyse non linéaire (2004)

  • Volume: 21, Issue: 3, page 341-379
  • ISSN: 0294-1449

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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 21.3 (2004): 341-379. <http://eudml.org/doc/78622>.

@article{Roussier2004,
author = {Roussier, Violaine},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {spherically symmetric perturbations},
language = {eng},
number = {3},
pages = {341-379},
publisher = {Elsevier},
title = {Stability of radially symmetric travelling waves in reaction–diffusion equations},
url = {http://eudml.org/doc/78622},
volume = {21},
year = {2004},
}

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
PB - Elsevier
VL - 21
IS - 3
SP - 341
EP - 379
LA - eng
KW - spherically symmetric perturbations
UR - http://eudml.org/doc/78622
ER -

References

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  1. [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. Zbl0325.35050MR427837
  2. [2] Aronson D.G., Weinberger H.F., Multidimensional nonlinear diffusion arising in population genetics, Adv. Math.30 (1978) 33-76. Zbl0407.92014MR511740
  3. [3] Fife P.C., Long time behaviour of solutions of bistable nonlinear diffusion equations, Arch. Rational Mech. Anal.70 (1979) 31-46. Zbl0435.35045MR535630
  4. [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. Zbl0361.35035MR442480
  5. [5] Fisher R.A., The advance of advantageous genes, Ann. of Eugenics7 (1937) 355-369. Zbl63.1111.04JFM63.1111.04
  6. [6] Henry D., Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math., vol. 840, Springer-Verlag, New York, 1981. Zbl0456.35001MR610244
  7. [7] Jones C.K.R.T., Spherically symmetric solutions of a reaction–diffusion equation, J. Differential Equations49 (1983) 142-169. Zbl0523.35059MR704268
  8. [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. Zbl0528.35054MR702830
  9. [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. MR157130
  10. [10] Kapitula T., Multidimensional stability of planar travelling waves, Trans. Amer. Math. Soc.349 (1997) 257-269. Zbl0866.35021MR1360225
  11. [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. [12] Levermore C.D., Xin J.X., Multidimensional stability of travelling waves in a bistable reaction–diffusion equation II, Comm. Partial Differential Equations17 (1992) 1901-1924. Zbl0789.35020MR1194744
  13. [13] Pazy A., Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983. Zbl0516.47023MR710486
  14. [14] Sattinger D.H., Weighted norms for the stability of travelling waves, J. Differential Equations25 (1977) 130-144. Zbl0315.35010MR447813
  15. [15] Taylor A.E., Introduction to Functional Analysis, Wiley, New York, 1961. Zbl0081.10202MR98966
  16. [16] Uchiyama K., Asymptotic behaviour of solutions of reaction–diffusion equations with varying drift coefficients, Arch. Rational Mech. Anal.90 (1983) 291-311. Zbl0618.35058MR801583
  17. [17] Xin J.X., Multidimensional stability of travelling waves in a bistable reaction–diffusion equation I, Comm. Partial Differential Equations17 (1992) 1889-1899. Zbl0789.35019MR1194743

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