Convergence to travelling waves for quasilinear Fisher-KPP type equations

J. I. Díaz*, S. Kamin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We consider the Cauchy problem{ut=φ(u)xx+ψ(u),(t,x)∈R+×R,u(0,x)=u0(x),x∈R, when the increasing function φ satisfies that φ(0)=0 and the equation may degenerate at u=0 (in the case of φ '(0)=0). We consider the case of u0∈L∞(R), 0≤u 0(x)≤1 a.e. x∈R and the special case of ψ(u)=u-φ(u). We prove that the solution approaches the travelling wave solution (with speed c=1), spreading either to the right or to the left, or to the two travelling waves moving in opposite directions.

Original languageEnglish
Pages (from-to)74-85
Number of pages12
JournalJournal of Mathematical Analysis and Applications
Volume390
Issue number1
DOIs
StatePublished - 1 Jun 2012

Funding

FundersFunder number
European Community’s
University of Central Missouri
Seventh Framework Programme238702
Seventh Framework Programme

    Keywords

    • Asymptotic convergence
    • Kolmogorov, Petrovsky and Piscunov equation
    • Travelling waves

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