| Abstract: |
| Variational inequalities with unknown-dependent constraints are called Quasivariational Inequalities (QVI). There are so many phenomena in the real world which are more preferable to describe them as QVIs rather than usual variational ones.However, it is not easy to formulate them rigorously and to solve them in a strong sense.
In this talk we propose a class of nonlinear evolution inclusions governed by time-dependent subdifferentials and semimonotone mappings in Banach spaces which includes parabolic QVIs in some weak variational sense. Our approach is based on the recent devepoment of theory of compactness theorem obtained by Gokieli-Kenmochi-Niezgodka and of nonlinear evolution inclusions. We give an existence result and application to the model of superconductivity which is a QVI with time-dependent gradient constraint depending on the unknown. |
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