Non-uniform Dependence on Initial Data for the Solutions of a b-Family System - LIANG Xiaowen; YU Shengqi (Nantong Daxue xuebao. Ziran kexue ban)
Aiming at the continuous property of solutions to the Cauchy problem of a b-family system in Besov spaces, a new type of approximate solutions containing high and low frequency terms is first constructed. Afterwards,the error estimates of approximate solutions are derived by applying energy methods. On the basis of it the difference between the equations of the approximate solutions and real solutions are computed, and the difference between the approximate and real solutions is also presented. Finally, by proving that the difference is negligible, one manages to prove that the solution to this equation is not uniformly continuous with respect to the initial data.