Time-Periodic Planar Fronts Around an Obstacle.

This paper is concerned with a time-periodic reaction-diffusion equation in exterior domains Ω = R N \ K , where K is a compact set in R N and is called an obstacle. We first prove the existence of the entire solution u(t, x) emanating from a time-periodic planar front ϕ (t , x 1 - c t) as t → - ∞ . Then, under the assumption that the propagation of u(t, x) is complete, we prove that u(t, x) converges to the same time-periodic planar front ϕ (t , x 1 - c t) as t → + ∞ uniformly in Ω ¯ . Finally, we show some examples of geometrical shapes of K such that the propagation of u(t, x) is complete or incomplete. [ABSTRACT FROM AUTHOR]