Emergence of waves in a nonlinear convection-reaction-diffusion equation

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Abstract

In this work we prove that for some class of initial data the solution of the Cauchy problem ut = (um)xx + a(u m)x + u(1 - um-1), x ∈ ℝ, t > 0 u(0, x) = u0(x), u0(x) ≥ 0 approaches the travelling solution, spreading either to the right or to the left, or two travelling waves moving in opposite directions.

Original languageEnglish
Pages (from-to)251-272
Number of pages22
JournalAdvanced Nonlinear Studies
Volume4
Issue number3
DOIs
StatePublished - Aug 2004

Keywords

  • Asymptotic behaviour of solutions
  • Nonlinear diffusion
  • Travelling waves

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