Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 475, Issue 1, Pages 278-312Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2019.02.042
Keywords
Maxwell's equations; Nonlinear boundary feedback; Instantaneous damping; Time-localized delay; Well-posedncss; Exponential stability
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Funding
- Deutsche Forschungsgemeinschaft (DFG) at Karlsruhe Institute of Technology, Germany [CRC 1173]
- University of Texas at El Paso, USA
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We consider an initial-boundary value problem for the Maxwell's system in a bounded domain with a linear nonhomogeneous anisotropic instantaneous material law subject to a nonlinear Silver-Muller-type boundary feedback mechanism incorporating both an instantaneous damping and a time-localized delay effect. By proving the maximal monotonicity property of the underlying nonlinear generator, we establish the global well-posedness in an appropriate Hilbert space. Further, under suitable assumptions and geometric conditions, we show the system is exponentially stable. (C) 2019 Elsevier Inc. All rights reserved.
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