摘要
考虑了一类带三阶粘性项的高维广义ＫｄＶ－Ｂｕｒｇｅｒｓ型方程组的周期边值问题和初值问题，利用先验估计及Ｇａｌｅｒｋｉｎ方法，证明了所论问题整体解的存在性、唯一性和正则性。在一定条件下讨论了这些问题的解当ｔ→＋∞时的渐近行为，给出了一类高维广义ＫｄＶ－Ｂｕｒｇｅｒｓ型方程解“爆破”的充分条件。
This paper deals with the periodic boundary value problem and the initial value problem for the system of multidimensional generalized KdV-Burgers equations with third order viscous term.The existence and uniqueness of the global solution for these problems are proved by the Galerkin method and a priori estimation.The asymptotic behaviour of the solution for the problem is investigated under certain conditions.The sufficient conditions are given for the existence of the blowing-up solution for a class of systems of multidimensional inhomogeneous generalized KdV-Burgers equations.
出处
《甘肃科学学报》
1996年第2期1-9,共9页
Journal of Gansu Sciences
关键词
周期边值问题
整体解
KDV-B方程
非线性波动
KdV-Burgers equation
BBM-Burgers equation
Periodic boundary value problem
Initial value problem
Global solution
Galerkin method
Asymptotic behavior
Blow up
