Large time behavior of solutions to a nonlinear integro-differential system

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. Initial–boundary 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.