一类非线性波动方程弱解的存在唯一性  

EXISTENCE OF WEAK SOLUTIONS FOR A CLASS OF NONLINEAR WAVE EQUATIOM

作　　者：陈金梅[1] 王祥[1] 

机构地区：[1]忻州师范学院数学系,忻州034000

出　　处：《系统科学与数学》2011年第8期985-991,共7页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金资助课题

摘　　要：在考虑强阻尼效应的情形下,建立了一类轴向载荷作用下的波动方程.研究一类具有强阻尼的非线性波动方程的初边值问题的整体解的性态.以Sobolev空间的性质为工具,利用Faedo-Galerkin方法,证明了该方程在线性边界条件下弱解的存在唯一性,为力学中具有阻尼结构的振动问题的研究提供了重要依据.In this paper, with the strong damping effect, a class of the wave equation with axial loading is considered. The properties of the global solutions for a class of strongly damped nonlinear wave equation with initial boundary value problem are investigated. Based on the Sobolev space properties and by using Faedo-Galerkin method, the existence of weak solutions of the equation with linear boundary conditions is proved, which provides an important basis for the research of vibration damping problem in mechanics.

关 键 词：非线性波动方程 GALERKIN方法 

分 类 号：O175.29[理学—数学]