Front propagation and blocking of reaction-diffusion systems in cylinders

In this paper, we consider a bistable monotone reaction-diffusion system in cylindrical domains. We first prove the existence of the entire solution emanating from a planar front. Then, it is proved that the entire solution converges to a planar front if the propagation is complete and the domain is bilaterally straight. Finally, we give some geometrical conditions on the domain such that the propagation of the entire solution is complete or incomplete, respectively.

Automated summary

This paper investigates a bistable monotone reaction-diffusion system in cylindrical domains. The existence of the entire solution emanating from a planar front is first proven, followed by showing the convergence of the entire solution to a planar front under certain conditions. Geometrical conditions on the domain for complete or incomplete propagation of the entire solution are also provided.