粘弹性边界条件弹性板的最优控制  

Optimal Control of an Elastic Plate with Viscoelastic Boundary Conditions

作　　者：付莲莲[1,2] 卢殿臣[2] 田立新[2] 顾建军[2] 黄斌 

机构地区：[1]江西农业大学理学院 [2]江苏大学理学院非线性科学研究中心,镇江212013 [3]江西都昌第一中学数学教研组

出　　处：《工程数学学报》2007年第1期50-54,共5页Chinese Journal of Engineering Mathematics

基　　金：江苏省自然科学基金(2000-65-31)

摘　　要：本文研究在给定空间控制特殊边界条件带加强项的弹性板的问题;首先用不动点原理证明状态方程解的相关正则性,运用Sobolev空间理论,Young、Gronwall、Holder等一些常用不等式得出状态方程弱解的先验估计:其次选择合适的目标函数,从前面得到的先验估计可以知道状态方程的解的范数在给定的空间有界,所以存在收敛子序列,由此证明最优控制的存在性。The problem for optimal control of an elastic plate with viscoelastic boundary conditions is considered. Firstly, we show the well-posedness of state equations by fixed-point theorem, and get an important priori estimate for solution for state problem using Sobolev space theory and Young, Gronwall, Holder inequalities. Secondly, we select appropriate object function, and prove the existness of optimal control in the corresponding space. Lastly, characterization for optimal controls is gotten by common methods in optimal control theory.

关 键 词：弹性板 粘弹性 最优控制 半群理论 不动点原理 

分 类 号：O193[理学—数学]