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Asymptotic behavior of the Maxwell equations in cylinders becoming unbounded in one direction. (English) Zbl 1462.35382

Summary: We consider the Maxwell equations in a cylinder as the length of the cylinder goes to infinity in the direction of an axis. We prove that when the datum is independent of the axial coordinate, the solution converges to a solution of the Maxwell equations in the infinite cylinder with the rate of convergence being exponential.

MSC:

35Q61 Maxwell equations
78A25 Electromagnetic theory (general)
35B40 Asymptotic behavior of solutions to PDEs
35P10 Completeness of eigenfunctions and eigenfunction expansions in context of PDEs
41A58 Series expansions (e.g., Taylor, Lidstone series, but not Fourier series)
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