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Uniform well-posedness for a time-dependent Ginzburg-Landau model in superconductivity. (English) Zbl 1420.35393

Summary: We study the initial boundary value problem for a time-dependent Ginzburg-Landau model in superconductivity. First, we prove the uniform boundedness of strong solutions with respect to diffusion coefficient \(0 < \epsilon < 1\) in the case of Coulomb gauge. Our second result is the global existence and uniqueness of the weak solutions to the limit problem when \(\epsilon=0\).

MSC:

35Q56 Ginzburg-Landau equations
35K55 Nonlinear parabolic equations
35D30 Weak solutions to PDEs
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
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References:

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