Entire solutions of combustion reaction-diffusion equations in exterior domains

Abstract

In this paper, we consider entire solutions of combustion reaction-diffusion equations in exterior domains. By constructing appropriate super- and sub-solutions, we show that any given transition front of homogeneous combustion reaction-diffusion equation can emanate an entire solution in exterior domains. In addition, we prove that the entire solution is a complete propagation in the exterior domain with some suitable spatial geometrical conditions.