Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 268, Issue 2, Pages 784-812Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2019.08.032
Keywords
Quasilinear Maxwell equations; Silver-Muller boundary conditions; Nonhomogeneous anisotropic materials; Global existence; Exponential stability
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Funding
- Deutsche Forschungsgemeinschaft (DFG) [CRC 1173]
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We investigate an initial-boundary value problem for a quasilinear nonhomogeneous, anisotropic Maxwell system subject to an absorbing boundary condition of Silver & Muller type in a smooth, bounded, strictly star-shaped domain of R-3. Imposing usual smallness assumptions in addition to standard regularity and compatibility conditions, a nonlinear stabilizability inequality is obtained by showing nonlinear dissipativity and observability-like estimates enhanced by an intricate regularity analysis. With the stabilizability inequality at hand, the classic nonlinear barrier method is employed to prove that small initial data admit unique classical solutions that exist globally and decay to zero at an exponential rate. Our approach is based on a recently established local well-posedness theory in a class of H-3-valued functions. (C) 2019 Elsevier Inc. All rights reserved.
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