Spreading solutions for a reaction diffusion equation with free boundaries in time-periodic environmen

Abstract

In this article, we consider a reaction diffusion equation with free boundaries in a time-periodic environment. Such models can be used to describe the spreading of a new or invasive species over a one-dimensional habitat, with the free boundaries representing the expanding fronts. We study an equation with a general time-periodic nonlinearity, and present some sufficient conditions for spreading phenomena. We also use time-periodic semi-waves to characterize the spreading solutions.

Keywords

• Spreading phenomenon
• free boundary
• time-periodic environment