A macroscopic model for an intermediate state between type‐I and type‐II superconductivity |
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| Authors: | Karel Van Bockstal Marián Slodi?ka |
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| Affiliation: | Department of Mathematical Analysis, Research Group NaM2, Ghent University, Ghent, Belgium |
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| Abstract: | A vectorial nonlocal and nonlinear parabolic problem on a bounded domain for an intermediate state between type‐I and type‐II superconductivity is proposed. The domain is for instance a multiband superconductor that combines the characteristics of both types. The nonlocal term is represented by a (space) convolution with a singular kernel arising in Eringen's model. The nonlinearity is coming from the power law relation by Rhyner. The well‐posedness of the problem is discussed under low regularity assumptions and the error estimate for a semi‐implicit time‐discrete scheme based on backward Euler approximation is established. In the proofs, the monotonicity methods and the Minty–Browder argument are used. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1551–1567, 2015 |
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| Keywords: | error estimates integro‐partial differential equation nonlinear parabolic equation nonlocal superconductors quasi‐static Maxwell's equations singular convolution kernel time discretization |
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