Numerical Analysis Seminars: Variational and quasi-variational inequalities for critical-state models in plasticity and supraconductivity
4 May 2001 00:00 in CM105
"Elliptic problems with gradient constraints arise naturally in the elastoplastic torsion of a bar. These problems are well understood in the framework of variational inequalities and may correspond to quasi-variational inequalities if the gradient bound depends on the solution itself. While the stationary problems may be solved by fixed point techniques, once the continuous dependence on the convex set is shown, the corresponding evolutionary problems are much more delicate to analyse, as those arising in some superconductivity models. For instance, in the Bean critical state problem, the gradient of the average magnetic field is constrained by a critical value. When this value is constant, the mathematical problem consists of a parabolic variational inequality which can be analysed and computed developing standard functional and numerical methods. In the physical variant in which that threshold may be a function of the magnetic field, the corresponding model is an evolutionary quasi-variational inequality. We survey a few known results for the variational problems and some of its variants, we describe the recent existence result for the quasi-variational inequality, obtained in a joint work with Lisa Santos."
Contact David.Bourne@durham.ac.uk for more information