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Existence of a solution to a coupled variational problem constraint by a function depending on the solution. (English) Zbl 1433.35032

Summary: We consider coupled variational inequality and variational equality, and a case where inequality is constrained by a function of a solution to the variational equality. We show the existence of a solution to the coupled system. The problem is related to the Bean critical-state model in type II superconductors with a thermal effect in a multi-connected domain. Mathematically, we are concerned with coupled variational inequality and variational equality containing a \(p\)-curl inequality constraint by a function of the solution to \(q\)-Laplacian equality.

MSC:

35J20 Variational methods for second-order elliptic equations
35H30 Quasielliptic equations
35D30 Weak solutions to PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
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