A semilinear interface problem arising from population genetics

Abstract We study a semilinear parabolic problem that models the evolution of gene frequencies under the joint action of migration and selection with a geographical barrier. The barrier locates at an embedded interface and is of Kedem-Katchalsky type. Our main goal is to investigate the effects of the barrier on the global dynamics and on the existence, stability, and profile of spatially nonconstant equilibria.