Stability of entire solutions emanating from bistable planar traveling waves in exterior domains

Abstract

This paper is devoted to the Lyapunov stability of entire solutions emanating from a planar front for bistable (bistable-type or multistable-type) reaction–diffusion equations in exterior domains Ω=RN∖K. Applying the super- and sub-solution method, we prove that the entire solution is Lyapunov stable under the small initial perturbations. In addition, the Lyapunov stability is independent of the geometrical conditions of the obstacle K.