| 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. |
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