Large deviations and the emergence of a logarithmic delay in a nonlocal linearised Fisher-KPP equation
arXiv:2204.06593 · doi:10.1016/j.na.2023.113465
Abstract
We study a variant of the Fisher-KPP equation with nonlocal dispersal. Using the theory of large deviations, we show the emergence of a "Bramson-like" logarithmic delay for the linearised equation with step-like initial data. We conclude that the logarithmic delay emerges also for the solutions of the nonlinear equation. Previous papers found very precise results for the nonlinear equation with strong assumptions on the decay of the kernel. Our results are less precise, but they are valid for all continuous symmetric thin-tailed kernels.
20 pages, 1 figure. Accepted for publication in Nonlinear Analysis
References in corpus (4)
- Front propagation into unstable states: Universal algebraic convergence towards uniformly translating pulled fronts
- A microscopic probabilistic description of a locally regulated population and macroscopic approximations
- Nonlocal anisotropic dispersal with monostable nonlinearity
- Minima in branching random walks