EXISTENCE AND PROPERTIES OF TRAVELING WAVES FOR DOUBLY NONLOCAL FISHER-KPP EQUATIONS.

We consider a reaction-diffusion equation with nonlocal anisotropic diffusion and a linear combination of local and nonlocal monostable-type reactions in a space of bounded functions on ℝd. Using the properties of the corresponding semi ow, we prove the existence of monotone traveling waves along those directions where the diffusion kernel is exponentially integrable. Among other properties, we prove continuity, strict monotonicity and expo- nential integrability of the traveling wave profiles. [ABSTRACT FROM AUTHOR]