Nonlocal anisotropic dispersal with monostable nonlinearity
arXiv:1106.4531 · doi:10.1016/j.jde.2007.11.002
Abstract
We study the travelling wave problem J\astu - u - cu' + f (u) = 0 in R, u(-\infty) = 0, u(+\infty) = 1 with an asymmetric kernel J and a monostable nonlinearity. We prove the existence of a minimal speed, and under certain hypothesis the uniqueness of the profile for c = 0. For c = 0 we show examples of nonuniqueness.