Generalized principal eigenvalues of elliptic operators and spreading speeds of Fisher-KPP equations in two-scale almost periodic media

This paper is concerned with the asymptotic behavior of the generalized principal eigenvalues of elliptic operators and spreading speeds of Fisher-KPP equations in two-scale almost periodic media where one scale is fixed and another one approaches zero or infinity. We transform the problem into the homogenization of certain effective Hamiltonian and then establish the asymptotic limits and the convergence rates. Based on the analysis of the asymptotic behavior of effective Hamiltonians, we investigate how the heterogeneity of the advection and growth rates affect on the propagation in the case where the media has very rapid or slow spatial oscillation: We show a normal scale perturbation of the growth rate with mean zero can accelerate the propagation in the media with rapid or slow oscillation; and an advection with slow oscillation and mean zero can decelerate the propagation in 1-D case.

• Publication year

  2025

• Venue

  Unknown venue

• Publication date

  2025-07-29

• Fields of study

  Mathematics, Physics

• Identifiers
  arXiv 2507.21870
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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