{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:41:13Z","timestamp":1787341273955,"version":"build-2736575974"},"reference-count":53,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"DOI":"10.13039\/501100002428","name":"Austrian Science Fund","doi-asserted-by":"publisher","award":["DOC 78"],"award-info":[{"award-number":["DOC 78"]}],"id":[{"id":"10.13039\/501100002428","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002428","name":"Austrian Science Fund","doi-asserted-by":"publisher","award":["P30054"],"award-info":[{"award-number":["P30054"]}],"id":[{"id":"10.13039\/501100002428","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Math."],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>We analyze the behavior of third-order-in-time linear and nonlinear sound waves in thermally relaxing fluids and gases as the sound diffusivity vanishes. The nonlinear acoustic propagation is modeled by the Jordan--Moore--Gibson--Thompson equation both in its Westervelt-type and in its Kuznetsov-type forms, that is, including general nonlinearities of quadratic type. As it turns out, sufficiently smooth solutions of these equations converge in the energy norm to the solutions of the corresponding inviscid models at a linear rate. Numerical experiments illustrate our theoretical findings.<\/jats:p>","DOI":"10.1137\/21m139390x","type":"journal-article","created":{"date-parts":[[2021,7,19]],"date-time":"2021-07-19T12:17:53Z","timestamp":1626697073000},"page":"1461-1482","source":"Crossref","is-referenced-by-count":21,"title":["The Inviscid Limit of Third-Order Linear and Nonlinear Acoustic Equations"],"prefix":"10.1137","volume":"81","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3295-6977","authenticated-orcid":true,"given":"Barbara","family":"Kaltenbacher","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vanja","family":"Nikoli\u0107","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,7,19]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1007\/s00033-018-0999-5"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1016\/0093-6413(80)90029-4"},{"key":"atypb3","first-page":"25","author":"Beyer R. 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Holm,\n                      Waves with Power-Law Attenuation\n                      , Springer, New York, 2019.","DOI":"10.1007\/978-3-030-14927-7"},{"key":"atypb15","doi-asserted-by":"crossref","first-page":"2189","DOI":"10.3934\/dcdsb.2014.19.2189","volume":"19","author":"Jordan P. M.","year":"2014","journal-title":"Discrete Contin. Dyn. Syst. Ser. B"},{"key":"atypb16","first-page":"971","volume":"40","author":"Kaltenbacher B.","year":"2011","journal-title":"Control Cybernet."},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202512500352"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202519500532"},{"key":"atypb19","unstructured":"B. Kaltenbacher and V. Nikoli\u0107,\n                      Parabolic Approximation of Quasilinear Wave Equations with Applications in Nonlinear Acoustics\n                      , preprint, arXiv:2011.07360, 2020."},{"key":"atypb20","first-page":"1","volume":"5","author":"Kaltenbacher B.","year":"2020","journal-title":"Pure Appl. Funct. Anal."},{"key":"atypb21","doi-asserted-by":"crossref","unstructured":"M. Kaltenbacher,\n                      Numerical Simulation of Mechatronic Sensors and Actuators\n                      , Vol. 3, Springer, New York, 2014.","DOI":"10.1007\/978-3-642-40170-1"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1016\/0022-1236(72)90003-1"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1155\/S1024123X03209017"},{"key":"atypb24","first-page":"467","volume":"16","author":"Kuznetsov V. P.","year":"1970","journal-title":"Soviet Phy. Acoust."},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1007\/s00028-016-0353-3"},{"key":"atypb26","unstructured":"J. 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