一類弱耗散b-族系統(tǒng)解的持續(xù)性研究

劉思淼 郁勝旗

摘 要：本文研究了一類帶有弱耗散項的b-族系統(tǒng)解的持續(xù)性問題。我們通過引入權(quán)重函數(shù)，運用能量方法證明了二元b-族系統(tǒng)的強解具備如下持續(xù)性質(zhì)：如果系統(tǒng)的初值是指數(shù)衰減的，那么在解的最大存在時刻內(nèi)，系統(tǒng)的解也是指數(shù)衰減的，并且衰減速率與初值相同。

關(guān)鍵詞：b-族系統(tǒng);權(quán)函數(shù);能量方法;持續(xù)性

Persistence property for a weakly dissipative b-family system

LIU Simiao ?YU Shengqi*

School of Science， Nantong University， Nantong 226019， China

Abstract： This paper mainly concerns about the persistence property of solution for a weakly dissipative b-family system. By introduction of the weight function， we use the energy method to prove that the strong solution to this system posses the following persistence property： If the initial data decays exponentially with respect to the spatial variable， then the solution will decay exponentially with the same rate during its maximum existence time.

Keywords： B-family system; Weight function; Energy method; Persistence property