一类偏微分积分方程解的稳定性

Stability for Partial Differentio-integral Equation

由于微分旋转的阻尼转矩作用在弹性梁上，Ｄ．ＬＲｕｓｓｅｌｌ建立了描述这种弹性梁的运动方程是一个偏微分积分方程。文中用线性算子半群方法证明了这种偏微分积分方程的解的存在唯一性，以及它的能量按指数衰减趋于零的稳定性。并且证明了相应的特征方程的每一个特征值都具有负实部。

Considering the damping torque in differential rotation acting on the elastic beam, D. L.Russell establish motion equation discribing the elastic beam that is one of the partial differentio-integral equation. In this paper,the existencity,uniqulity and stability of the solution for the solution for the equation,and every eegenvalue of the characteristic equation corresponding the partiai differentio-integral equation are proved to have negative real part.