可控二维平面驻波的边值混合问题

Mixed Boundary Value Problem of Controlled Two-dimensional Plane Standing Wave

主要研究一类二维Poisson方程的边值混合问题.通过分离变量法,计算混合问题的具有Fourier级数形式的解;寻求边界条件中的函数能够展开成Fourier正弦级数的条件;最后,通过该问题Fourier级数形式解的能量积分定义,说明平面驻波混合问题的可控性.

The mixed boundary value problem of a class of two dimensional Passon equation is studied in this paper. Through the method of separation of variables, the solution to the mixed problem is attained in Fourier series form. The boundary conditions of functions which can be expanded as Fourier series are sought. The energy integral definition of the Fourier series form demonstrates the controllability of mixed problems of the two - dimensional plane standing wave.