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On a degenerate evolution system associated with the Bean critical-state for type II superconductors. (English) Zbl 1470.82039

Summary: We study a degenerate evolution system containing the \(p\)-curl system in a bounded domain with initial and boundary conditions for the magnetic field \(\mathbf{H}\) under the influence of a system force \(\mathbf{F}\). This is concerned with an approximation of Bean’s critical-state model for type II superconductors. We will show the existence, uniqueness, and regularity of solutions. Moreover we will get the properties of the limit solution as \(p \to \infty\).

MSC:

82D55 Statistical mechanics of superconductors
78A48 Composite media; random media in optics and electromagnetic theory
35Q60 PDEs in connection with optics and electromagnetic theory
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