Unique solvability for high-frequency heterogeneous time-harmonic Maxwell equations via the Fredholm alternative theory
1998; Wiley; Volume: 21; Issue: 6 Linguagem: Inglês
10.1002/(sici)1099-1476(199804)21
ISSN1099-1476
Autores Tópico(s)Advanced Mathematical Modeling in Engineering
ResumoMathematical Methods in the Applied SciencesVolume 21, Issue 6 p. 463-477 Research Article Unique solvability for high-frequency heterogeneous time-harmonic Maxwell equations via the Fredholm alternative theory Ana Alonso, Corresponding Author Ana Alonso Dipartimento di Matematica, Università di Trento, 38050 Povo (Trento), ItalyDipartimento di Matematica, Università di Trento, 38050 Povo (Trento), Italy===Search for more papers by this authorAlberto Valli, Alberto Valli Dipartimento di Matematica, Università di Trento, 38050 Povo (Trento), ItalySearch for more papers by this author Ana Alonso, Corresponding Author Ana Alonso Dipartimento di Matematica, Università di Trento, 38050 Povo (Trento), ItalyDipartimento di Matematica, Università di Trento, 38050 Povo (Trento), Italy===Search for more papers by this authorAlberto Valli, Alberto Valli Dipartimento di Matematica, Università di Trento, 38050 Povo (Trento), ItalySearch for more papers by this author First published: 04 December 1998 https://doi.org/10.1002/(SICI)1099-1476(199804)21:6 3.0.CO;2-UCitations: 9AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Abstract We consider the time-harmonic Maxwell equations in the high-frequency case for a heterogeneous medium, i.e., a medium which is composed by a conductor and a perfect insulator, or, in other words, a loaded cavity. As a consequence of a suitable compactness result, we prove that Fredholm alternative holds for such a problem. Since the kernels of the considered operator and of its adjoint are proven to be trivial, a unique solution exists for each given datum. © 1998 B. G. Teubner Stuttgart–John Wiley & Sons Ltd. References 1 Alonso, A. and Valli, A., 'Some remarks on the characterization of the space of tangential traces of H(rot; ω) and the construction of an extension operator', Manuscr. Math., 89, 159–178 (1996). 2 Alonso, A. and Valli, A., 'A domain decomposition Approach for Heterogeneous Time-Harmonic Maxwell Equations', Comput. Meth. Appl. Mech. Eng., 143, 97–112 (1997). 3 Bendali, A., Dominguez, J. M. and Gallic, S., 'A variational approach for the vector potential formulation of the Stokes and Navier-Stokes problems in three-dimensional domains', J. Math. Anal. Appl., 107, 537–560 (1985). 4 Bossavit, A., Électromagnétisme, en Vue de la Modélisation, Springer, Paris 1993. 5 Foias, C. and Temam, R., 'Remarques sur les équations de Navier-Stokes stationnaires et les phénomènes successifs de bifurcations', Ann. Scuola Norm. Sup. Pisa, 5 (IV), 29–63 (1978). 6 Girault, V. and Raviart, P.-A., Finite Element Methods for Navier-Stokes Equations. Theory and Algorithms, Springer, Berlin, 1986. 7 Leis, R., ' Exterior boundary-value problems in mathematical physics', in: Trends in Applications of Pure Mathematics to Mechanics, ( H. Zorski, ed.), Vol. 11, pp. 187–203, Pitman, London, 1979. 8 Leis, R., Initial Boundary Value Problems in Mathematical Physics, Wiley, Chichester, 1986. 9 Picard, R., 'On the boundary value problems of electro- and magnetostatics', Proc. Royal Soc. Edinburgh, 92A, 165–174 (1982). 10 Saranen, J., 'On generalized harmonic fields in domains with anisotropic nonhomogeneous media', J. Math. Anal. Appl., 88, 104–115 (1982). Erratum: J. Math. Anal. Appl., 91, 300 (1983). 11 Weber, C. A., 'A local compactness theorem for Maxwell's equations', Math. Meth. Appl. Sci., 2, 12–25 (1980). 12 Witsch, K. J., 'A remark on a compactness result in electromagnetic theory', Math. Meth. Appl. Sci., 16, 123–129 (1993). Citing Literature Volume21, Issue6April 1998Pages 463-477 ReferencesRelatedInformation
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