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A macroscopic model for an intermediate state between type‐I and type‐II superconductivity
Author(s) -
Van Bockstal Karel,
Slodička Marián
Publication year - 2015
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21959
Subject(s) - mathematics , type (biology) , bounded function , monotonic function , domain (mathematical analysis) , nonlinear system , mathematical analysis , euler's formula , superconductivity , kernel (algebra) , convolution (computer science) , backward euler method , pure mathematics , euler equations , physics , quantum mechanics , ecology , machine learning , artificial neural network , computer science , biology
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