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A new and improved analysis of the time domain boundary integral operators for the acoustic wave equation. (English) Zbl 1361.65075

Summary: 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 Calderón projector for the wave equation and can be generalized to other relevant boundary integral equations.

MSC:

65M38 Boundary element methods for initial value and initial-boundary value problems involving PDEs
35L05 Wave equation
65J08 Numerical solutions to abstract evolution equations
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
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