{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:14:31Z","timestamp":1787321671166,"version":"build-2736575974"},"reference-count":37,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Math. Anal."],"published-print":{"date-parts":[[2024,6,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>In this work, we investigate a mathematical model of nonlinear ultrasonic heating based on a coupled system of the Westervelt equation and the hyperbolic Pennes bioheat equation (Westervelt\u2013Pennes\u2013Cattaneo model). Using the energy method together with a fixed point argument, we prove that our model is locally well-posed and does not degenerate under a smallness assumption on the pressure data in the Westervelt equation. In addition, we perform a singular limit analysis and show that the Westervelt\u2013Pennes\u2013Fourier model can be seen as an approximation of the Westervelt\u2013Pennes\u2013Cattaneo model as the relaxation parameter tends to zero. This is done by deriving uniform bounds of the solution with respect to the relaxation parameter.<\/jats:p>","DOI":"10.1137\/23m1564134","type":"journal-article","created":{"date-parts":[[2024,5,2]],"date-time":"2024-05-02T04:04:06Z","timestamp":1714622646000},"page":"2968-3003","source":"Crossref","is-referenced-by-count":4,"title":["The Westervelt\u2013Pennes\u2013Cattaneo Model of Nonlinear Thermo\u2013Acoustics: Local Well\u2013Posedness and Singular Limit for Vanishing Relaxation Time"],"prefix":"10.1137","volume":"56","author":[{"given":"Imen","family":"Benabbas","sequence":"first","affiliation":[{"name":"AMNEDP Laboratory, Faculty of Mathematics, USTHB, Bab Ezzouar, 16111, Algiers, Algeria."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4876-2293","authenticated-orcid":true,"given":"Belkacem","family":"Said-Houari","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Sciences, University of Sharjah, Sharjah, United Arab Emirates."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2024,5,2]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1121\/1.406819"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-46079-2_9"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1007\/s00028-020-00654-2"},{"key":"ref4","first-page":"83","volume":"3","author":"Cattaneo C.","year":"1948","journal-title":"Atti. 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