An indefinite nonlinear diffusion problemin population genetics,II: Stability and multiplicity

Yuan Lou, Wei Meng Ni, Linlin Su

Research output: Contribution to journalArticle

30 Scopus citations

Abstract

We study a genetic model with two alleles A1and A2in a bounded smooth habitatω. The frequency u of the allele A1, under the combined influence of migration and selection, obeys a parabolic equation of the type Math equiten presented where δdenotes the Laplace operator, g may change sign in ω, and f(0) = f(1) = 0,f(s) >0 for sε(0,1). Our main results include stability/instability of the trivial steady states uξO and uξ1, and the multiplicity of nontrivial steady states. This is a continuation of our work [12]. In particular, the conjecture of Nagylaki and Lou [11, p. 152] has been largely resolved. Similar results are obtained for Dirichiet and Robin boundary value problems as well.

Original languageEnglish (US)
Pages (from-to)643-655
Number of pages13
JournalDiscrete and Continuous Dynamical Systems
Volume27
Issue number2
DOIs
StatePublished - Jun 1 2010

Keywords

  • Diffusion equations
  • Indefinite nonlinearity
  • Multiplicity
  • Stability

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