变耗散系数的柱Burgers方程和球Burgers方程的精确解  

Exact Solution of a Cylindrical Burgers Equation and a Spherical Equation with Variable Dissipative Coefficient

作　　者：李向正[1] 李伟[1] 王明亮[1,2] 

机构地区：[1]河南科技大学数学与统计学院,河南洛阳471023 [2]兰州大学数学系,甘肃兰州730000

出　　处：《应用数学》2017年第2期392-395,共4页Mathematica Applicata

基　　金：国家自然科学基金(11301153);河南科技大学博士启动基金项目(09001562)

摘　　要：根据简化齐次平衡原则,导出一个由线性方程的解到一个具变耗散系数的柱Burgers方程解的非线性变换.该线性方程容许有指数函数形式的解,因而借助所导出的非线性变换,获得一个具变耗散系数的柱Burgers方程的精确解.完全类似地,也获得一个具变耗散系数的球Burgers方程的精确解.Based on the simplified homogeneous balance principle, a nonlinear transformation that forms the solution of a linear equation to the solution of a cylindrical Burgers equation with variable dissipative coefficient has been derived. Since the linear equation admits an exponential type solution,substituting it into the nonlinear transformation derived here, we have had the exact solution of the cylindrical Burgers equation with variable dissipative coefficient. This method can be used to obtain the exact solution of a spherical Burgers equation with variable dissipative coefficient too.

关 键 词：柱Burgers方程 球Burgers方程 简化齐次平衡原则 精确解 

分 类 号：O175.2[理学—数学]