Local wellposedness of quasilinear Maxwell equations with absorbing boundary conditions

Schnaubelt R, Spitz M (2021)
Evolution Equations and Control Theory 10(1): 155-198.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Schnaubelt, Roland; Spitz, MartinUniBi
Abstract / Bemerkung
In this article we provide a local wellposedness theory for quasilinear Maxwell equations with absorbing boundary conditions in H-m for m >= 3. The Maxwell equations are equipped with instantaneous nonlinear material laws leading to a quasilinear symmetric hyperbolic first order system. We consider both linear and nonlinear absorbing boundary conditions. We show existence and uniqueness of a local solution, provide a blow-up criterion in the Lipschitz norm, and prove the continuous dependence on the data. In the case of nonlinear boundary conditions we need a smallness assumption on the tangential trace of the solution. The proof is based on detailed apriori estimates and the regularity theory for the corresponding linear problem which we also develop here.
Stichworte
Nonlinear Maxwell system; absorbing or impedance boundary conditions; local wellposedness; blow-up criterion; continuous dependence
Erscheinungsjahr
2021
Zeitschriftentitel
Evolution Equations and Control Theory
Band
10
Ausgabe
1
Seite(n)
155-198
eISSN
2163-2480
Page URI
https://pub.uni-bielefeld.de/record/2950200

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Schnaubelt R, Spitz M. Local wellposedness of quasilinear Maxwell equations with absorbing boundary conditions. Evolution Equations and Control Theory . 2021;10(1):155-198.
Schnaubelt, R., & Spitz, M. (2021). Local wellposedness of quasilinear Maxwell equations with absorbing boundary conditions. Evolution Equations and Control Theory , 10(1), 155-198. doi:10.3934/eect.2020061
Schnaubelt, R., and Spitz, M. (2021). Local wellposedness of quasilinear Maxwell equations with absorbing boundary conditions. Evolution Equations and Control Theory 10, 155-198.
Schnaubelt, R., & Spitz, M., 2021. Local wellposedness of quasilinear Maxwell equations with absorbing boundary conditions. Evolution Equations and Control Theory , 10(1), p 155-198.
R. Schnaubelt and M. Spitz, “Local wellposedness of quasilinear Maxwell equations with absorbing boundary conditions”, Evolution Equations and Control Theory , vol. 10, 2021, pp. 155-198.
Schnaubelt, R., Spitz, M.: Local wellposedness of quasilinear Maxwell equations with absorbing boundary conditions. Evolution Equations and Control Theory . 10, 155-198 (2021).
Schnaubelt, Roland, and Spitz, Martin. “Local wellposedness of quasilinear Maxwell equations with absorbing boundary conditions”. Evolution Equations and Control Theory 10.1 (2021): 155-198.

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