Nonuniform Dependence on Initial Data of a Periodic Camassa-Holm System

This paper is concerned with some properties of a periodic two-component Camassa-Holm system. By constructing two sequences of solutions of the two-component Camassa-Holm system, we prove that the solution map of the Cauchy problem of the two-component Camassa-Holm system is not uniformly continuous in Hs (), s>5/2

Planar Waves of the Buffered Bistable System

This paper is concerned with the large time behavior of disturbed planar fronts in the buffered bistable system in ℝn (n≥2). We first show that the large time behavior of the disturbed fronts can be approximated by that of the mean curvature flow with a drift term for all large time up to t=+∞. And then we prove that the planar front is asymptotically stable in L∞(ℝn) under ergodic perturbations, which include quasiperiodic and almost periodic ones as special cases