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Stability properties of multidimensional symmetric hyperbolic systems with damping, differential constraints and delay

Part of: Partial differential equations Hyperbolic equations and systems

Published online by Cambridge University Press:  07 September 2023

Gilbert Peralta Open the ORCID record for Gilbert Peralta [Opens in a new window]
Gilbert Peralta*
Affiliation:
Department of Mathematics and Computer Science, University of the Philippines Baguio, Governor Pack Road, Baguio, 2600 Philippines, (grperalta@up.edu.ph)
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Abstract

Multidimensional linear hyperbolic systems with constraints and delay are considered. The existence and uniqueness of solutions for rough data are established using Friedrichs method. With additional regularity and compatibility on the initial data and initial history, the stability of such systems are discussed. Under suitable assumptions on the coefficient matrices, we establish standard or regularity-loss type decay estimates. For data that are integrable, better decay rates are provided. The results are applied to the wave, Timoshenko, and linearized Euler–Maxwell systems with delay.

Keywords

Hyperbolic systemsdifferential constraintstime-delayFriedrichs methodasymptotic stabilityenergy methoddecay estimates

MSC classification

Primary: 35B35: Stability
Secondary: 35B40: Asymptotic behavior of solutions 35L40: First-order hyperbolic systems
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , First View , pp. 1 - 43
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Copyright
Copyright © The Author(s), 2023. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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