一类半线性卷积积分微分方程的初边值问题

INITIAL-BOUNDARY VALUE PROBLEMS FOR A CLASS OF SEMILINEAR CONVOLUTIONAL INTEGRO-DIFFERENTIAL EQUATIONS

本文考虑具线性粘弹性杆受粘性阻尼的横振动所引出的积分微分方程的初边值问题。在某些条件下，得到了解的存在性、唯一性、稳定性和正则性的结论。

This paper is devoted to study of the following initial-boundary value problem which comes from the mathematical model for nonlinear transverse vibrations of finite rods with linear viscoelasticity. The existence, uniqueness, stability and smoothness properties of the solution of this problem are obtained.