中文摘要：

考虑弹性理论中对边简支矩形薄板方程,用算子半群方法求解问题.首先,将方程转换成抽象Cauchy问题.其次,构造空间框架并证明对应的算子矩阵生成压缩半群.最后,经Fourier变换,采用一致连续半群做逼近,进而给出对边简支矩形薄板方程的解析解.该方法自然蕴含着解的存在唯一性.

英文摘要：

The problem of solving a rectangular thin plate with 2 opposite sides simply supported in elasticity theory by means of the operator semigroup method was addressed. First,the plate equations were transformed into the abstract Cauchy problem. Then,the Hilbert space was defined and it was proved that the corresponding operator matrix generates contraction semigroups. Finally,the uniformly continuous semigroup approximation was applied through the Fourier transform,and the analytical solutions to the equations were given. The method naturally implies the existence and uniqueness of the solution.