Local wellposedness of quasilinear Maxwell equations with conservative interface conditions
Schnaubelt R, Spitz M (2022)
Communications in Mathematical Sciences 20(8): 2265-2313.
Zeitschriftenaufsatz
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Autor*in
Schnaubelt, Roland;
Spitz, MartinUniBi 
Einrichtung
Abstract / Bemerkung
We establish a comprehensive local wellposedness theory for the quasilinear Maxwell system with interfaces in the space of piecewise H-m-functions for m >= 3. The system is equipped with instantaneous and piecewise regular material laws and perfectly conducting interfaces and boundaries. We also provide a blow-up criterion in the Lipschitz norm and prove the continuous dependence on the data. The proof relies on precise a priori estimates and the regularity theory for the corresponding linear problem also shown here.
Erscheinungsjahr
2022
Zeitschriftentitel
Communications in Mathematical Sciences
Band
20
Ausgabe
8
Seite(n)
2265-2313
ISSN
1539-6746
eISSN
1945-0796
Page URI
https://pub.uni-bielefeld.de/record/2967431
Zitieren
Schnaubelt R, Spitz M. Local wellposedness of quasilinear Maxwell equations with conservative interface conditions. Communications in Mathematical Sciences. 2022;20(8):2265-2313.
Schnaubelt, R., & Spitz, M. (2022). Local wellposedness of quasilinear Maxwell equations with conservative interface conditions. Communications in Mathematical Sciences, 20(8), 2265-2313. https://doi.org/10.4310/CMS.2022.v20.n8.a6
Schnaubelt, Roland, and Spitz, Martin. 2022. “Local wellposedness of quasilinear Maxwell equations with conservative interface conditions”. Communications in Mathematical Sciences 20 (8): 2265-2313.
Schnaubelt, R., and Spitz, M. (2022). Local wellposedness of quasilinear Maxwell equations with conservative interface conditions. Communications in Mathematical Sciences 20, 2265-2313.
Schnaubelt, R., & Spitz, M., 2022. Local wellposedness of quasilinear Maxwell equations with conservative interface conditions. Communications in Mathematical Sciences, 20(8), p 2265-2313.
R. Schnaubelt and M. Spitz, “Local wellposedness of quasilinear Maxwell equations with conservative interface conditions”, Communications in Mathematical Sciences, vol. 20, 2022, pp. 2265-2313.
Schnaubelt, R., Spitz, M.: Local wellposedness of quasilinear Maxwell equations with conservative interface conditions. Communications in Mathematical Sciences. 20, 2265-2313 (2022).
Schnaubelt, Roland, and Spitz, Martin. “Local wellposedness of quasilinear Maxwell equations with conservative interface conditions”. Communications in Mathematical Sciences 20.8 (2022): 2265-2313.
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