a b s t r a c tThe large-time behavior of solutions and finite difference approximations of the nonlinear integro-differential equation associated with the penetration of a magnetic field into a substance are studied. Asymptotic properties of solutions for the initial-boundary value problem with homogeneous Dirichlet boundary conditions is considered. The rates of convergence are given too. The convergence of the semidiscrete and the finite difference schemes are also proved.Published by Elsevier Ltd

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Asymptotic behavior of solutions as t → ∞Asymptotic behavior of solutions as t → ∞ to the nonlinear integro-differential system associated with the penetration of a magnetic field into a substance is studied. Initialboundary value problems with two kinds of boundary data are considered. The first with homogeneous conditions on whole boundary and the second with non-homogeneous boundary data on one side of lateral boundary. The rates of convergence are given too.

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