Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 532, Issue 1, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2023.127915
Keywords
Quasilinear Maxwell system; Absorbing boundary conditions; Nonhomogenous anisotropic; materials; Trace regularity; Exponential decay
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This study investigates the quasilinear Maxwell system with a strictly positive, state dependent boundary conductivity. The results demonstrate the existence of solutions for small data, which decay exponentially to 0. The improvement in results is achieved by introducing a new trace estimate, an observability-type estimate, and a detailed regularity analysis.
We study the quasilinear Maxwell system with a strictly positive, state dependent boundary conductivity. For small data we show that the solution exists for all times and decays exponentially to 0. As in related literature we assume a nontrapping condition. Our approach relies on a new trace estimate for the corresponding non-autonomous linear problem, an observability-type estimate, and a detailed regularity analysis. The results are improved in the linear autonomous case, using properties of the Helmholtz decomposition in Sobolev spaces of (small) negative order.(c) 2023 Elsevier Inc. All rights reserved.
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