Can Be Controlled Tow Dimensions Steady-State Wave With Mixed Boundary Problem

In the paper, we studied the following two dimensional Poisson equationwith Fourier series solution, used the energy of the solution to discuss the relation controlling problem,these problems are with strongly Physically background.(1) Given an interval at x-axis in the region on xy-plane, then there exists an interval at y-axis such that we can control the solution energy on the interval at y-axis.(2) Given an interval at y-axis in the region on xy-plane,then there exists an interval at x-axis such that we can control the solution energy on the interval at x-axis.This is an nonhomogeneous equation with nonhomogeneous boundary conditions,it is difficult to study these problems. First we used the properties of linear equations to divide the problem (0.1) with the following two problems andUsed the method of separation of variables and the properties of Possion equation to get the solutions of problems(0.2) and (0.3),then we get the solution of (0.1),at least we get our rssults.