Convergence to the travelling wave solution for a nonlinear reaction-diffusion equation
Kamin, Shoshana ; Rosenau, Philip
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 15 (2004), p. 271-280 / Harvested from Biblioteca Digitale Italiana di Matematica

We study the behaviour of the solutions of the Cauchy problem ut=umxx+u1-um-1,xR,t>0u0,x=u0x,u0x0, and prove that if initial data u0x decay fast enough at infinity then the solution of the Cauchy problem approaches the travelling wave solution spreading either to the right or to the left, or two travelling waves moving in opposite directions. Certain generalizations are also mentioned.

Publié le : 2004-12-01
@article{RLIN_2004_9_15_3-4_271_0,
     author = {Shoshana Kamin and Philip Rosenau},
     title = {Convergence to the travelling wave solution for a nonlinear reaction-diffusion equation},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {15},
     year = {2004},
     pages = {271-280},
     zbl = {1113.35094},
     mrnumber = {2148885},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_2004_9_15_3-4_271_0}
}
Kamin, Shoshana; Rosenau, Philip. Convergence to the travelling wave solution for a nonlinear reaction-diffusion equation. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 15 (2004) pp. 271-280. http://gdmltest.u-ga.fr/item/RLIN_2004_9_15_3-4_271_0/

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