# Some initial boundary problems in electrodynamics for canonical domains in quaternions

Mathematica Bohemica (2001)

- Volume: 126, Issue: 2, page 429-442
- ISSN: 0862-7959

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topMeister, Erhard V., and Meister, L.. "Some initial boundary problems in electrodynamics for canonical domains in quaternions." Mathematica Bohemica 126.2 (2001): 429-442. <http://eudml.org/doc/248847>.

@article{Meister2001,

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.},

author = {Meister, Erhard V., Meister, L.},

journal = {Mathematica Bohemica},

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; complex quaternions; initial-boundary transmission problems; Wiener-Hopf pseudodifferential systems; anisotropic Leontovitch boundary conditions; semi-infinite domains},

language = {eng},

number = {2},

pages = {429-442},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Some initial boundary problems in electrodynamics for canonical domains in quaternions},

url = {http://eudml.org/doc/248847},

volume = {126},

year = {2001},

}

TY - JOUR

AU - Meister, Erhard V.

AU - Meister, L.

TI - Some initial boundary problems in electrodynamics for canonical domains in quaternions

JO - Mathematica Bohemica

PY - 2001

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 126

IS - 2

SP - 429

EP - 442

AB - 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.

LA - eng

KW - electromagnetic fields by complex quaternions; initial boundary transmission problems for semi-infinite domains; reduction to Wiener-Hopf pseudo-differential systems; anisotropic Leontovitch boundary conditions; complex quaternions; initial-boundary transmission problems; Wiener-Hopf pseudodifferential systems; anisotropic Leontovitch boundary conditions; semi-infinite domains

UR - http://eudml.org/doc/248847

ER -

## References

top- Electrodynamics. A Modern Geometric Approach, Progress in Physics Vol. 17, Birkhäuser, Boston, 1999. (1999) Zbl0920.35149MR1711172
- Clifford Analysis, Pitman, Boston, 1982. (1982) MR0697564
- Inverse Acoustic and Electromagnetic Scattering Theory, Applied Mathematical Sciences Vol. 93, Springer Verlag, 1992. (1992) MR1183732
- On Sommerfeld’s half-plnae problem for the equations of linear themoelasticity, Math. Methods Appl. Sci. 18 (1995), 1215–1237. (1995) MR1362939
- Quaternionic and Clifford Calculus for Physicists and Engineers, Math. Methods in Practice, John Wiley & Sons, Chichester, 1997. (1997)
- Multivectors and Clifford Algebra in Electrodynamics, World Scientific Publ., Singapore, 1988. (1988) Zbl0727.15015MR1022883
- The Theory of Electromagnetism, International Series of Monographs on Pure and Applied Mathematics Vol. 47, Pergamon Press, New York, 1964. (1964) Zbl0121.21604MR0161555
- Investigations on Radiowave Propagation, Part II, Printing House Academy of Science, 1948. (1948)
- Inversion formula for the Sommerfeld integral, Sov. Phys. Dokl. 3 (1958), 52–56. (1958)
- Initial-Boundary Value Problems in Linear Viscoelasticity Using Wiener-Hopf Methods, PhD thesis, TU Darmstadt, 2000. (2000) Zbl0976.74002
- Clifford algebras and Maxwell’s equations in Lipschitz domains, Math. Methods Appl. Sci. 22 (1999), 1599–1620. (1999) MR1727215
- New results on wave diffraction by canonical obstacles, Oper. Theory Adv. Appl. 110 (1999), 235–256. (1999) MR1747897
- Modern Wiener-Hopf methods in diffraction theory, Ordinary and Partial Differential Equations, Vol. 2, B. Sleeman, R. J. Jarvis (eds.), Proc. Conf. Dundee 1988, Pitman Research Notes in Math., Longman, Harlow, 1989. (1989) MR1031728
- Quaternions and Their Application in Photogrammetry and Navigation, Habilitationsschrift. TU Bergakademie, Freiberg, 1998. (1998) Zbl0928.15009
- Sommerfeld-Halbebenenproblem mit elektromagnetisch anisotropen Leontovich-Randbedingungen, PhD thesis, TU Darmstadt, 1998. (1998)
- Diffraction of Plane Waves and Exact Time-Space Solutions for Some Linear Models in Classical Physics, Habilitationsschrift. TU Darmstadt, 2000. (2000)
- Clifford Algebras in Analysis and Related Topics. Based on a conference, Fayetteville, AR, 1993, CRC Press, Boca Raton, FL, 1996. (1996) MR1383097
- Elektromagnetische Grundgleichungen in bivektorieller Behandlung, Ann. Physik 22 (1907), 579–586. (1907)

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