带有耗散项的KdV-Burgers方程的适定性研究  

Well-posedness of the KdV-Burgers Equation with Dissipation

作　　者：孙海霞 Sun Haixia(School of Computer Science,Sichuan Technology and Business University,Chengdu 611745 China)

机构地区：[1]四川工商学院计算机学院,四川成都611745

出　　处：《四川工商学院学术新视野》2020年第2期35-38,68,共5页Academic New Vision of Sichuan Technology and Business University

摘　　要：文章研究带有耗散项Ly(u)的KdV-Burgers方程的柯西问题。首先,利用压缩映像原理和半群得到KdV-Burgers方程柯西问题的局部适定性。其次,基于能量积分估计,对满足特定条件的耗散项Ly(u)得到KdV-Burgers方程的整体适定性,即对满足一定条件的Y,KdV-Burgers方程在H^1(R)中存在整体解.最后,文章研究了KdV Burgers方程解的L^2(R)范数的指数衰减性号的标点都是错的!文章里全是错的。This paper studies the Cauchy problem of the KdV-Burgers equation with dissipative term.The local well-posedness for the Cauchy problem of the KdV-Burgers equation are obtained with the help of semigroup theory and the contraction mapping theorem.Based on the energy estimates,under some assumptions for the dissipative term,the global well-posedness of the KdV-Burgers equation for the dissipative term that satisfy certain conditions are established.Finally,the exponential decay of the norm of the solutions to the Cauchy problem of the KdV-Burgers equation is also presented.

关 键 词：KDV-BURGERS方程 耗散项 适定性 衰减性 

分 类 号：O175[理学—数学]