Fading memory spaces and approximate cycles in linear viscoelasticity
We prove the existence and find necessary and sufficient conditions for the uniqueness of the time-periodic solution to the equations for an arbitrary (sufficiently smooth) periodic right-hand side , where denotes the Laplace operator with respect to , and is the Ishlinskii hysteresis operator. For this equation describes e.g. the vibrations of an elastic membrane in an elastico-plastic medium.
In the paper, we deal with the equation of a rectangular thin plate with a simply supported boundary. The restoring force being an odd superlinear function of the vertical displacement, the existence of infinitely many nonzero time-periodic solutions is proved.
The paper deals with the problem of quasistatic frictionless contact between an elastic body and a foundation. The elasticity operator is assumed to vanish for zero strain, to be Lipschitz continuous and strictly monotone with respect to the strain as well as Lebesgue measurable on the domain occupied by the body. The contact is modelled by normal compliance in such a way that the penetration is limited and restricted to unilateral contraints. In this problem we take into account adhesion which...