Global Stability of Non-critical Traveling Fronts for a Belousov-Zhaboti nskii Model with Time Delay

Abstract

This paper is concerned with the traveling fronts of a Belousov-Zhabotinskii system with a time delay. The stability of the traveling fronts with large speeds is proved by Meng et al. [1]. However, the stability of all waves, including the slower waves (i.e., the wave speed near the critical wave speed), for such a system is unsolved. In this paper, we show that all traveling fronts with non-critical wave speeds are exponentially asymptotically stable. The exponential convergent rate is also obtained.