The hair-trigger effect for a class of nonlocal nonlinear equations

Abstract

We prove the hair-trigger effect for a class of nonlocal nonlinear evolution equations on ${\mathbb{R}}^d$ which have only two constant stationary solutions, $0$ and $\theta >0$. The effect consists in that the solution with an initial condition non identical to zero converges (when time goes to $\infty$) to $\theta$ locally uniformly in ${\mathbb{R}}^d$. We find also sufficient conditions for existence, uniqueness and comparison principle in the considered equations.

To appear in 'Nonlinearity'

References in corpus (6)

• A microscopic probabilistic description of a locally regulated population and macroscopic approximations
• Nonlocal anisotropic dispersal with monostable nonlinearity
• Pulsating fronts for nonlocal dispersion and KPP nonlinearity
• Traveling waves and long-time behavior in a doubly nonlocal Fisher-KPP equation
• Point-wise estimates for nonlocal heat kernel of convolution type operators
• Phase Transitions in a Logistic Metapopulation Model with Nonlocal Interactions