第二类四阶变分不等式解的存在唯一性  

The Existence and Uniqueness of the Solution for the Fourth-order Variational Inequality of the Second Kind

作　　者：崔玉环[1] 陈一鸣[1] 曾凤霞[1] 李绕[1] 

机构地区：[1]燕山大学理学院,秦皇岛066004

出　　处：《数学理论与应用》2008年第1期55-59,共5页Mathematical Theory and Applications

基　　金：河北省自然科学基金(E2007000381)资助

摘　　要：本文考虑弹性力学平板理论中的单侧稳定问题,讨论了重调和方程边值问题及第二类四阶变分不等式,并证明它们的等价性,从而可以把高阶偏微分方程转化为相应的变分不等式加以解决,同时也为求解重调和方程提供了更多的方法和理论依据。并且最后给出了该类变分不等式解的存在唯一性的证明。A four- order variational inequality of the second kind,deduced from plate bonding problems with friction term, is considered and the boundary value problem of biharmonic equation is discussed and their equality is proved. So the high - order partial differential equation can be solved by the corresponding variational inequality. Also these works provide more methods and the theoretical basis for solving biharmonic equation.At last, the existence and uniqueness of the solution for the variational inequality of this kind is proved.

关 键 词：第二类四阶变分不等式 重调和方程 边值问题 存在唯一性 

分 类 号：O175.2[理学—数学]