一类广义KdV－Burgers型方程的初边值问题

Initial Boundary Value Problem for a Class of the Generalized KdV-Burgers Type Equations

本文研究了一类带三阶粘性项的广义ＫｄＶ－Ｂｕｒｇｅｒｓ型方程的初边值问题．运用Ｇａｌｅｒｋｉｎ逼近方法，结合能量估计，得到了问题整体解的存在性，正则性，唯一性和稳定性等结果．并在一定条件下讨论了问题的解的渐近行为和“爆破”现象．

This paper considers the initial-boundary value problem for the generalized KdV-Burgers equations with the third order viscous term. The existence and uniqueness of the global solution for the problem are proved by means of a priority estimation and the Galerkinmethod. The asymptotic behavior and 'blow up' Phenomenon of the solution for the problem are inverstigated under certain conditions.