接触问题边界变分不等式解的存在唯一性

The Existence and Uniqueness of Solution of Boundary Variational Inequality for Contact Problem

以Signorini接触问题为背景,讨论了变分不等式与边值问题的等价性,利用Green公式,基本解和基本解法向导数的性质,将二维区域上的边值问题化为等价的边界变分不等式,并证明了边界变分不等式解的存在唯一性。

In this paper, backgrounded on the Signorini contact problem, the equality between variational inequality and boundary value problems is studied. By use of Green formula, the foundamental solution and normal derivative of the solution, the boundary value problems in the two-dimensional domain into an equivalent boundary variational inequality is reduced, and the existence and uniqueness of solution of boundary variational inequality is proved.