a1 Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA (email@example.com)
a2 Department of Mathematics, National Taiwan Normal University, Taipei 116, Taiwan (firstname.lastname@example.org)
a3 Department of Applied Mathematics and Informatics, Ryukoku University, Seta, Otsu 520-2194, Japan (email@example.com)
This paper deals with entire solutions of a bistable reaction—diffusion equation for which the speed of the travelling wave connecting two constant stable equilibria is zero. Entire solutions which behave as two travelling fronts approaching, with super-slow speeds, from opposite directions and annihilating in a finite time are constructed by using a quasi-invariant manifold approach. Such solutions are shown to be unique up to space and time translations.
(Received December 08 2004)
(Accepted December 13 2005)