Parabolic Approximation to Variational Problems with Double Obstacles

AbstractIn this paper, we discuss an elliptic variational inequality with double obstacles in a finite interval which can be rewritten as a nonlinear boundary value problem. We use a parabolic initial-boundary value problem to approximate it and prove that every smooth solution of the variational problem can be regarded as a limit of a smooth solution of a parabolic problem. From the viewpoint of numerical computation, parabolic equations are easy and can be solved using extremely stable standard computer routines. Therefore, our result is useful both for the theory of differential equations and for the numerical computation