Multitype branching Brownian motion and traveling waves

Abstract

In this article we study the parabolic system of equations which is closely related to a multitype branching Brownian motion. Particular attention is paid to the monotone traveling wave solutions of this system. Provided with some moment conditions, we show the existence, uniqueness, and asymptotic behaviors of such waves with speed greater than or equal to a critical value c̲ and nonexistence of such waves with speed smaller than c̲.