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MATHEMATICA BOHEMICA, Vol. 126, No. 2, pp. 429-442 (2001)
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# Some initial boundary problems in electrodynamics for canonical domains in quaternions

## E. Meister, L. Meister

* E. Meister*, * L. Meister*, Tieckstr. 6, 64291 Darmstadt, Germany, e-mail: ` meister@mathematik.tu-darmstadt.de`

**Abstract:**
The initial boundary-transmission problems for electromagnetic fields in homogeneous and anisotropic media for canonical semi-infinite domains, like halfspaces, wedges and the exterior of half- and quarter-plane obstacles are formulated with the use of complex quaternions. The time-harmonic case was studied by A. Passow in his Darmstadt thesis 1998 in which he treated also the case of an homogeneous and isotropic layer in free space and above an ideally conducting plane. For thin layers and free space on the top a series of generalized vectorial Leontovich boundary value conditions were deduced and systems of Wiener-Hopf pseudo-differential equations for the tangential components of the electric and magnetic field vectors and their jumps across the screens were formulated as equivalent unknowns in certain anisotropic boundary Sobolev spaces. Now these results may be formulated with alternating differential forms in Lorentz spaces or with complex quaternions.

**Keywords:** electromagnetic fields by complex quaternions, initial boundary transmission problems for semi-infinite domains, reduction to Wiener-Hopf pseudo-differential systems, anisotropic Leontovitch boundary conditions

**Classification (MSC2000):** 35Q60, 78A45, 35J20

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