On the transition from initial data to travelling waves in the fisher-kpp equation
Titel:
On the transition from initial data to travelling waves in the fisher-kpp equation
Auteur:
Sherratt, Jonathan A.
Verschenen in:
Dynamical systems
Paginering:
Jaargang 13 (1998) nr. 2 pagina's 167-174
Jaar:
1998
Inhoud:
The Fisher-KPP equation [image omitted] has a travelling wave solution for all speeds [image omitted] . Initial data that decrease monotonically from 1 to 0 on [image omitted] , with [image omitted] as [image omitted] , are known to evolve to a travelling wave, whose speed depends on [image omitted] . Here, it is shown that the relationship between wave speed and [image omitted] , can be recovered by linearizing the Fisher-KPP equation about [image omitted] and explicitly solving the linear equation. Moreover, the calculation predicts that in the case [image omitted] , the solution for [image omitted] itself evolves to a transition wave, moving ahead of the (minimum speed) u wave at the greater speed of [image omitted] . Behind this transition[image omitted] , while ahead of it[image omitted] . The paper goes on to discuss the potential applications of the method to systems of coupled reaction-diffusion equations
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