In the recent thirty years, a great of investigations have been made in the Wiener-Hopf equations and variational inequalities as two mutually independent problems. In this paper, we investigate the equivalenee of the...In the recent thirty years, a great of investigations have been made in the Wiener-Hopf equations and variational inequalities as two mutually independent problems. In this paper, we investigate the equivalenee of the solution of variational inequality and the inversion of the Toeplitz operator when the projection operators P, Q are linear. The solution of general Wiener-Hopf equation is coneluded as the solution of a variational problem. Thus an approximation method of obtaining the maximum value by variational is proposed to obtain the approximation of general Wiener-Hopf equation and apply it to the spaee eontaet problems in the elastieity theory. Espeeially, the solution representation is given in ease that the projection of eontaet surfaee is round. The dosing-form solution is also given when the known displaeement is a polynomial of even power.展开更多
基金This research is supported by National Natural Science Foundation of China (69972036) Shaanxi Province's Natural Science Research Project (2000SL03).
基金National "863" Program Project(2007AA01Z410)the Elitist D Class Project of Beijing(20071D050700175)
文摘In the recent thirty years, a great of investigations have been made in the Wiener-Hopf equations and variational inequalities as two mutually independent problems. In this paper, we investigate the equivalenee of the solution of variational inequality and the inversion of the Toeplitz operator when the projection operators P, Q are linear. The solution of general Wiener-Hopf equation is coneluded as the solution of a variational problem. Thus an approximation method of obtaining the maximum value by variational is proposed to obtain the approximation of general Wiener-Hopf equation and apply it to the spaee eontaet problems in the elastieity theory. Espeeially, the solution representation is given in ease that the projection of eontaet surfaee is round. The dosing-form solution is also given when the known displaeement is a polynomial of even power.
