非线性边界条件下具非线性耗散粘弹性梁方程的整体解

摘要

考虑材料的粘性效应和非线性外阻尼,对一类轴向载荷和横向载荷作用下具非线性耗散项的粘弹性梁方程进行研究,采用 Galerkin 方法,证明了该方程在非线性边界条件下整体解的存在唯一性.%In this paper,we establish one kind of nonlinear viscous-elastic supported beam subj ected to axial forces and transverse load,considering both viscosity effect and nonlinear ex-ternal daming,and obtain the existence and uniqueness theorem of global solutions for the equa-tions under nonlinear boundary conditions by the Galerkin approach.