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Mathematical analysis of absorbing boundary conditions for the wave equation: the corner problem


Author: Olivier Vacus
Journal: Math. Comp. 74 (2005), 177-200
MSC (2000): Primary 78A40, 65N12; Secondary 65M12, 46N40
DOI: https://doi.org/10.1090/S0025-5718-04-01669-2
Published electronically: July 22, 2004
MathSciNet review: 2085407
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Abstract: Our goal in this work is to establish the existence and the uniqueness of a smooth solution to what we call in this paper the corner problem, that is to say, the wave equation together with absorbing conditions at two orthogonal boundaries. First we set the existence of a very smooth solution to this initial boundary value problem. Then we show the decay in time of energies of high order--higher than the order of the boundary conditions. This result shows that the corner problem is strongly well-posed in spaces smaller than in the half-plane case. Finally, specific corner conditions are derived to select the smooth solution among less regular solutions. These conditions are required to derive complete numerical schemes.


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Additional Information

Olivier Vacus
Affiliation: CEA/CESTA, 33 114 Le Barp Cedex, France
Email: vacus.olivier@wanadoo.fr

DOI: https://doi.org/10.1090/S0025-5718-04-01669-2
Keywords: Wave equation, absorbing boundary conditions, domain with a corner, energy methods, strong well-posedness, stability
Received by editor(s): May 26, 2002
Received by editor(s) in revised form: June 29, 2003
Published electronically: July 22, 2004
Article copyright: © Copyright 2004 American Mathematical Society