Well-Posedness of a Nonlocal Stage-Structured Population Model with Free Boundary^§

Abstract

We propose a delay-induced nonlocal free boundary problem by modeling the invasion of a two-stage structured species, where the nonlocal interaction is caused jointly by time delay, free boundary and the diffusion. After establishing a comparison principle and a priori boundedness estimates, we prove the local and global existence of classical solutions for the model.

Keywords

Reaction-diffusion equation / free boundary / time delay