On unilateral contact problems with friction for an elastic body with cracks (Analysis of inverse problems through partial differential equations and related topics)

Abstract

This expository article deals with contact problems with friction for a linearized (visco) elasticity in two dimension, which are arising from a wide variety of phenomena in mechanical engineering and concerning with some inverse problems and control problems. Contact conditions for cracks are so-called non-penetration conditions defined as unilateral conditions on the displacements of bodies to exclude nonphysical phenomenon such as mutual penetration of crack faces, see [11] for the details. In the present paper, mathematical results obtained in [9] and [5] are introduced and moreover, dynamic unilateral contact problems are discussed.