The hair-trigger effect for a class of nonlocal nonlinear equations - Dmitri Finkelshtein (Nonlinearity, 2018)
We prove the hair-trigger effect for a class of nonlocal nonlinear evolution equations on R^d which have only two constant stationary solutions, 0 and θ>0. The effect consists in that the solution with an initial condition non identical to zero converges (when time goes to ∞) to θ locally uniformly in R^d. We find also sufficient conditions for existence, uniqueness and comparison principle in the considered equations.