On rate-independent hysteresis models
The authors develop a general approach based on energy principles for studying rate-independent processes with hysteresis. The involved energy functionals are the potential energy \(I(t,z)\) and the dissipation \(\Delta(\dot{z})\), where \(z\) is the variable describing the process and \(\dot{z}\) is the time variable, assuming that \(\Delta\) is homogeneous of degree 1 for ensuring the rate-independence. In the convex case, the authors' formulation becomes an inclusion problem in terms of subdifferential which is stated as \(0\in\partial\Delta(\dot{z})+\partial I(t,z)\). Various results for existence, uniqueness and temporal smoothness of solutions are given.
scientific article; zbMATH DE number 2123247