摘要
Ｂｕｒｇｅｒｓ万程ｕ’＋αｕｕｘ＋γｕｘｘ＝０是可积的、典型的非线性耗散波方程．本文就具时间系数的Ｂｕｒｇｅｒｓ方程的初边值向题，用Ｒｉｅｍａｎｎ函数方法设计一恰当结构，利用Ｇｒｅｅｎ公式及定解条件获得一与之相等价的积分微分方程，并依Ｂａｎａｃｈ不动点原理，由该积分微分方程序列而得本定解问题一致收敛的迭代解．
The Burgers equation is an integrable and typical nolinear dissipative wave equation. In this paper a proper structure is established for the initial boundary value problem of the Burgers eqution with time coefficeient by means of the Riemann functional method. An integral and differential equation which is equal to the value of Burgers equation is given by utilizing Green formula and the fixed solution conditiom. Then according to the Banach fixed point principle and uniformly convergent interative solution of this fixed solution problem is acquired from the integral and differential equation sequence.
出处
《哈尔滨师范大学自然科学学报》
1994年第2期10-15,共6页
Natural Science Journal of Harbin Normal University
关键词
时间系数
伯格斯方程
初边值问题
Riemann Function
Structure, Fixed point, Integral differential equation
Uniform convergence
