ASYMPTOTIC SOLUTION OF A VARIATIONAL INEQUALITY MODELING FRICTION

Abstract

The problem of minimizing the nondifferentiable functional is considered. An asymptotic solution of the corresponding variational inequality is constructed and justified under the assumption that or is a small parameter. Also, formal asymptotic representations are obtained for singular surfaces which characterize a change in the type of boundary conditions. For a modification of the Vishik-Lyusternik method is used, and exponential boundary layers arise. If , then the boundary layer has only power growth; the principal term of the asymptotic expansion of the solution of the problem in a multidimensional region and the complete asymptotic expansion for the case are obtained.