{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T15:02:59Z","timestamp":1776783779185,"version":"3.51.2"},"reference-count":18,"publisher":"American Mathematical Society (AMS)","issue":"249","license":[{"start":{"date-parts":[[2005,7,22]],"date-time":"2005-07-22T00:00:00Z","timestamp":1121990400000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>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\u2014higher 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.<\/p>","DOI":"10.1090\/s0025-5718-04-01669-2","type":"journal-article","created":{"date-parts":[[2004,9,20]],"date-time":"2004-09-20T09:57:53Z","timestamp":1095674273000},"page":"177-200","source":"Crossref","is-referenced-by-count":17,"title":["Mathematical analysis of absorbing boundary conditions for the wave equation: the corner problem"],"prefix":"10.1090","volume":"74","author":[{"given":"Olivier","family":"Vacus","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2004,7,22]]},"reference":[{"issue":"2","key":"1","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1137\/0727021","article-title":"Second-order absorbing boundary conditions for the wave equation: a solution for the corner problem","volume":"27","author":"Bamberger, Alain","year":"1990","journal-title":"SIAM J. Numer. 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Vacus, Stabilit\u00e9 de conditions aux limites pour l\u2019\u00e9quation des ondes par des m\u00e9thodes \u00e9nerg\u00e9tiques: le cas des bords courbes, INRIA Rocquencourt technical report 2849, France, 1996."},{"issue":"3","key":"14","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1016\/S0764-4442(00)88592-4","article-title":"Un r\u00e9sultat d\u2019existence et d\u2019unicit\u00e9 pour l\u2019\u00e9quation de Helmholtz avec conditions aux limites absorbantes d\u2019ordre 2","volume":"329","author":"Joly, Patrick","year":"1999","journal-title":"C. R. Acad. Sci. Paris S\\'{e}r. I Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0764-4442","issn-type":"print"},{"key":"15","doi-asserted-by":"publisher","first-page":"703","DOI":"10.2307\/2004572","article-title":"Stability theory for difference approximations of mixed initial boundary value problems. I","volume":"22","author":"Kreiss, Heinz-Otto","year":"1968","journal-title":"Math. 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