高阶椭圆方程的Lie对称及不变解

Lie Symmetries and Invariant Solutions of Higher Order Elliptic Equations

对2维高阶线性椭圆方程进行了Lie对称分析.给出该方程拥有的无穷维Lie代数及其核心7维子Lie代数的1阶优化系统;构造了该椭圆方程对应优化系统的约化及不变精确解.最后给出了Lie代数在该方程初边值问题求解上的应用.

A Lie symmetry analysis is given for 2-dimensional linear elliptic equations.The infinite dimensional Lie algebra admitted by the equations is found and a one-dimensional optimal system of its 7-dimensional key sub-algebra is constructed.The symmetry reductions and invariant exact solutions for the equations with respect to the optimal system are given.At last,the applications of the symmetry method on the boundary value problems of the elliptic equations are investigated.