Convergence to the travelling wave solution for a nonlinear reaction-diffusion equation

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Abstract

We study the behaviour of the solutions of the Cauchy problem ut = (um)xx + u(1 - um-1), xεR, t > 0 u(0, x) = u0(x), u0(x) ≥ 0, and prove that if initial data u0(x) 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.

Original languageEnglish
Pages (from-to)271-280
Number of pages10
JournalAtti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica E Applicazioni
Volume15
Issue number3-4
StatePublished - 2004

Keywords

  • Asymptotic behaviour of solutions
  • Nonlinear diffusion
  • Reaction-diffusion equation
  • Travelling waves

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