Special Session 18: Advanced methodologies in mathematical materials science and biology

Quasi-variational inequalities for superconductivity model

Nobuyuki Kenmochi
Department of Mathematics, Chiba University
Japan
Co-Author(s):    Maria Gokieli, Marek Niezgodka
Abstract:
In this talk we treat a quasi-variational model of superconductivity, which was introduced by L. Prigozhin in 1996, under unknown dependent constraints. Our model is a coupled system of a parabolic variational inequality with gradient constraint for a magnetic field and a heat equation, interacting each other. Our approach is based on the general theory on parabolic quasi-variational inequalities in abstract Banach spaces evolved by the author with the co-authors in the last eight years. We give an existence result of weak solutions of the system in a variational sense. In the proof we make use the concept of time-derivative operators associated with unknown dependent constraints as well as a compactness theorem for parabolic variational inequalities.