A nonlocal parabolic model for type‐I superconductors

Abstract

A vectorial nonlocal linear parabolic problem on a bounded domain with applications in superconductors of type‐I is studied. The nonlocal term is represented by a (space) convolution with a singular kernel (arising in Eringen's model). The well‐posedness of the problem is discussed under low regularity assumptions, and the error estimates for an implicit and semiimplicit time‐discrete scheme (based on backward Euler approximation) are established. It is shown that the solution of the problem satisfies a simpler nonlocal problem with a positive definite kernel if the normal component of the unknown vector field equals zero on the boundary of the domain. Numerical experiments support the obtained theoretical results. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1821–1853, 2014