On the nonlocal Fisher-KPP equation: steady states, spreading speed and global bounds

Abstract

We consider the Fisher-KPP equation with a non-local interaction term. We establish a condition on the interaction that allows for existence of non-constant periodic solutions, and prove uniform upper bounds for the solutions of the Cauchy problem, as well as upper and lower bounds on the spreading rate of the solutions with compactly supported initial data.

Cited by in corpus (6)

• Global existence, asymptotic behavior, and pattern formation driven by the parametrization of a nonlocal Fisher-KPP problem
• Spatial nonhomogeneous periodic solutions induced by nonlocal prey competition in a diffusive predator-prey model
• The hair-trigger effect for a class of nonlocal nonlinear equations
• Quasiparticles for the one-dimensional nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation
• Bifurcations and dynamics emergent from lattice and continuum models of bioactive porous media
• Branching random walk with non-local competition