Resident-invader dynamics in infinite dimensional systems

These types of questions were first proposed and studied by S. Geritz et al. [20] and S. Geritz [19] for a class of ordinary differential equations. We extend and generalize previous work in two directions. Firstly, we consider analytic semiflows in infinite-dimensional spaces. Secondly, we devise an argument based on Hadamard's graph transform method that does not depend on the monotonicity of the two-species system. Our results are applicable to a wide class of reaction-diffusion models as well as models with nonlocal diffusion operators.