Backward Global Solutions Characterizing Annihilation Dynamics of Travelling Fronts

  • Hiroki Yagisita

    Kyoto University, Japan

Abstract

We consider a reaction-diffusion equation , where has exactly three zeros , and , , and . Then, the equation has a travelling wave solution with and . Known results suggest that for an initial state with having two interfaces at a large distance, approaches a pair of travelling wave solutions for a long time, and then the travelling fronts eventually disappear by colliding with each other. While our results establish this process, they show that there is a (backward) global solution and that the annihilation process is approximated by a solution .

Cite this article

Hiroki Yagisita, Backward Global Solutions Characterizing Annihilation Dynamics of Travelling Fronts. Publ. Res. Inst. Math. Sci. 39 (2003), no. 1, pp. 117–164

DOI 10.2977/PRIMS/1145476150