一类三阶偏微分方程的对称约化  

Symmetry Reduction of a Class of Third-order Partial Differential Equations

作　　者：李吉娜[1] 杨静[1] 陈媛媛[1] 郭得锋[2] LI Ji-Na1, YANG Jing1, CHEN Yuan-Yuan1, GUO De-Feng2(1. College of Science, Zhong yuan University of Technology, Zhengzhou 450007, China;2. School of Energy and Environment, Zhong yuan University of Technology, Zhengzhou 450007)

机构地区：[1]中原工学院理学院,河南郑州450007 [2]中原工学院能源与环境学院,河南郑州450007

出　　处：《数学的实践与认识》2018年第14期287-292,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(天元)项目(11626238);河南省高等学校重点科研项目(18A110036,17A110037,15B110012)

摘　　要：主要利用广义条件对称方法研究一类三阶偏微分方程的对称约化问题，首先给出所研究三阶偏微分方程允许的广义条件对称的分类，并根据所允许的对称将偏微分方程的初值问题约化为常微分方程的初值问题并得到其解．This paper studies the symmetry reduction of a class of third-order partial differential equations by generalized conditional symmetry. Firstly, the symmetry classification of the third-order partial differential equations which admit certain types of GCS is obtained and reduce the initial-value problem of PDEs to the IVP of ordinary differential equations, and the solutions are obtained.

关 键 词：对称分类 偏微分方程 初值问题 广义条件对称 

分 类 号：O175.2[理学—数学]