具有结构阻尼的梁振动方程解的存在性

发布时间：2018-03-16 00:16

本文选题：C_0-半群　切入点：梁振动方程　出处：《兰州交通大学》2017年硕士论文　论文类型：学位论文

【摘要】：本文主要研究具有结构阻尼的梁振动方程解的存在性.本文共分为四章.在第一章中,我们简要介绍了本文的研究背景,本文主要工作以及课题研究所要用到的定义和基本结果.其中包括算子半群理论,非紧性测度理论,凝聚映射和凝聚映射的不动点定理,渐近周期函数的概念和基本性质.第二章讨论了具有结构阻尼的梁振动方程初值问题mild解的全局存在性.在Banach空间中,当非线性项f满足一定的限制条件时,运用算子半群理论和Leray-Schauder不动点定理,建立了mild解的全局存在性定理.此外,我们还给出了所得mild解的H¨older正则性结果.最后,给出了具体的应用实例来阐释我们所得结果的可行性.第三章,我们主要研究梁振动方程非局部问题mild解的存在性,在紧半群情形下给出了梁振动方程非局部问题mild解的半群表示形式,并且借助非紧性测度理论以及不动点定理得到了解的存在性结果.第四章考虑梁振动方程渐近周期解的存在性.我们利用线性算子的半群理论和不动点定理,得到了上述方程解存在的充分条件.同时也给出了具体的例子来阐释我们所得的结论的可行性.
[Abstract]:There are beam vibration equations of this paper is mainly concerned with the structural damping. This paper is divided into four chapters. In the first chapter, we briefly introduce the research background of this paper, the main work of this paper is to use the research and the definition and basic results. Including semigroup theory, measure of noncompactness theory and the fixed point theorem of condensing mapping and condensing mapping, the concept of asymptotically periodic functions and basic properties. The second chapter discusses the existence of global mild equations of beam with structural damping solution. In Banach space, when the nonlinear term satisfies certain f constraints, by using semigroup theory and Leray-Schauder the fixed point theorem, establish the global existence theorem of solutions of mild. In addition, we also give the solution of mild H "older regularity results. Finally, an application example is given to illustrate our specific. The fruit is feasible. The third chapter, we mainly study the beam vibration equation of nonlocal problem for the existence of mild solutions, in the case of compact semigroup is given the beam vibration equation of nonlocal problem for the mild semigroup representation, and obtain the existence of the solutions of non Compactness Measure Theory and fixed point theorem. In the fourth chapter, by means of solving beam vibration equations considering the existence of asymptotically periodic. We use the theory of Semigroups of linear operators and fixed point theorem, sufficient conditions are obtained for the solution of the above equation is feasible. At the same time also gives specific examples to explain our conclusions.

【学位授予单位】：兰州交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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