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2017 A new and improved analysis of the time domain boundary integral operators for the acoustic wave equation
Matthew E. Hassell, Tianyu Qiu, Tonatiuh Sánchez-Vizuet, Francisco-Javier Sayas
J. Integral Equations Applications 29(1): 107-136 (2017). DOI: 10.1216/JIE-2017-29-1-107

Abstract

We present a novel analysis of the boundary integral operators associated to the wave equation. The analysis is done entirely in the time-domain by employing tools from abstract evolution equations in Hilbert spaces and semi-group theory. We prove a single general theorem from which well-posedness and regularity of the solutions for several boundary integral formulations can be deduced as specific cases. By careful choices of continuous and discrete spaces, we are able to provide a concise analysis for various direct and indirect formulations, both for their Galerkin in space semi-discretizations and at the continuous level. Some of the results here are improvements on previously known results, while other results are equivalent to those in the literature. The methodology presented greatly simplifies analysis of the operators of the Calder\'on projector for the wave equation and can be generalized to other relevant boundary integral equations.

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Matthew E. Hassell. Tianyu Qiu. Tonatiuh Sánchez-Vizuet. Francisco-Javier Sayas. "A new and improved analysis of the time domain boundary integral operators for the acoustic wave equation." J. Integral Equations Applications 29 (1) 107 - 136, 2017. https://doi.org/10.1216/JIE-2017-29-1-107

Information

Published: 2017
First available in Project Euclid: 27 March 2017

zbMATH: 1361.65075
MathSciNet: MR3628109
Digital Object Identifier: 10.1216/JIE-2017-29-1-107

Subjects:
Primary: 65J08 , 65M38 , 65R20

Keywords: abstract evolution equations , Galerkin BEM , Retarded boundary integral equations

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.29 • No. 1 • 2017
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