Journal of Integral Equations and Applications

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, and Francisco-Javier Sayas

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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.

Article information

Source
J. Integral Equations Applications, Volume 29, Number 1 (2017), 107-136.

Dates
First available in Project Euclid: 27 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.jiea/1490583473

Digital Object Identifier
doi:10.1216/JIE-2017-29-1-107

Mathematical Reviews number (MathSciNet)
MR3628109

Zentralblatt MATH identifier
1361.65075

Subjects
Primary: 65J08: Abstract evolution equations 65M38: Boundary element methods 65R20: Integral equations

Keywords
Retarded boundary integral equations Galerkin BEM abstract evolution equations

Citation

Hassell, Matthew E.; Qiu, Tianyu; Sánchez-Vizuet, Tonatiuh; Sayas, Francisco-Javier. A new and improved analysis of the time domain boundary integral operators for the acoustic wave equation. J. Integral Equations Applications 29 (2017), no. 1, 107--136. doi:10.1216/JIE-2017-29-1-107. https://projecteuclid.org/euclid.jiea/1490583473


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