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

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.