一类具有黏阻尼的非线性弹性杆方程的初边值问题  

Initial-boundary Value Problems for a Kind of Nonlinear Elastic Rods with Some Suitable Damped

作　　者：牛丽芳[1] 张建文[1] 

机构地区：[1]太原理工大学数学学院,太原030024

出　　处：《太原理工大学学报》2014年第1期128-132,共5页Journal of Taiyuan University of Technology

基　　金：国家自然科学基金资助项目(11172194);国家自然科学基金数学天元青年基金资助项目(11226316);山西省青年科技研究基金资助项目(2011021002-2);山西省自然科学基金资助项目(2010011008)

摘　　要：在给定的Sobolve空间中,研究了一类非线性弹性杆方程的初边值问题,其中非线性项具有临界增长指数。描述了考虑非线性势力作用下具有黏阻尼的弹性杆的振动问题,利用Faedo-Galerkin方法,通过对变系数及非线性的处理,证明了该系统在一定初边值条件下整体弱解的存在、唯一性。为此类力学振动问题的研究和计算提供了理论依据。The initial-boundary value problem was studied in given Sobolve space, where the nonlinear term satisfies a critical exponential growth condition. The problem involves a class of nonlinear partial differential equations describing the nonlinear elastic rods with viscous damp under external force. By using Faedo-Galerkin method, the existence and uniqueness of the weak solutions for the proposed problem were proved through the appropriate manipulation of variable coefficient and nonlinear items.

关 键 词：Faedo—Galerkin方法 黏阻尼 非线性弹性杆 初边值问题 

分 类 号：O19[理学—数学]