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Article

Jangveladze, Temur A. ; Kiguradze, Zurab V.
Asymptotics for large time of solutions to nonlinear system associated with the penetration of a magnetic field into a substance. (English). Applications of Mathematics, vol. 55 (2010), issue 6, pp. 471-493
MSC: 35B40, 35K51, 35K55, 35Q61, 45K05, 74H40, 78A30 | MR 2737715 | Zbl 1224.35189 | DOI: 10.1007/s10492-010-0019-3
Keywords:
system of nonlinear integro-differential equations; magnetic field; asymptotics for large time
Summary:
The nonlinear integro-differential system associated with the penetration of a magnetic field into a substance is considered. The asymptotic behavior as $t\to \infty $ of solutions for two initial-boundary value problems are studied. The problem with non-zero conditions on one side of the lateral boundary is discussed. The problem with homogeneous boundary conditions is studied too. The rates of convergence are given. Results presented show the difference between stabilization characters of solutions of these two cases.
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