Hysteresis and hemivariational inequalities: Semilinear case (Q1272990)

The authors study a semilinear parabolic boundary value problem with a continuous hysteresis operator. The formulation of the problem leads to a hemivariational inequality. This fact has a strong physical motivation allowing mechanical laws which contain nonmonotone discontinuities. A basic example is provided by the semipermeability problem with hysteretic effects. Two general existence results are established according to different growth conditions that are used. The approach relies on time-discretization, a priori estimates, regularization, truncation and limit procedure.