{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:34:14Z","timestamp":1787319254844,"version":"build-2736575974"},"reference-count":36,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","funder":[{"DOI":"10.13039\/100012740","name":"Gruppo Nazionale per l'Analisi Matematica, la Probabilit\u00e0 e le loro Applicazioni","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100012740","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Math. Anal."],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>We study the dynamics of viscoelastic materials coupled by a common cohesive interface (or, equivalently, two single domains separated by a prescribed cohesive crack) in the anti-plane setting. We consider a general class of traction-separation laws featuring an activation threshold on the normal stress, softening, and elastic unloading. In the strong form, the evolution is described by a system of PDEs coupling momentum balance (in the bulk) with transmission and Karush--Kuhn--Tucker conditions (on the interface). We provide a detailed analysis of the system. We first prove the existence of a weak solution, employing a time discrete approach and a regularization of the initial data. Then, we prove our main results: the energy identity and the existence of solutions with acceleration in $L^\\infty (0,T; L^2)$. Thanks to the latter we finally prove the existence of strong solutions satisfying the balance of forces in the bulk and on the interface.<\/jats:p>","DOI":"10.1137\/20m1355823","type":"journal-article","created":{"date-parts":[[2021,10,5]],"date-time":"2021-10-05T11:43:27Z","timestamp":1633434207000},"page":"5682-5730","source":"Crossref","is-referenced-by-count":2,"title":["Existence, Energy Identity, and Higher Time Regularity of Solutions to a Dynamic Viscoelastic Cohesive Interface Model"],"prefix":"10.1137","volume":"53","author":[{"given":"Matteo","family":"Negri","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7217-7417","authenticated-orcid":true,"given":"Riccardo","family":"Scala","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,10,5]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2012.32.1125"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1051\/cocv\/2016014"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1016\/S0065-2156(08)70121-2"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1007\/s002050050135"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202508002942"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1051\/cocv\/2009037"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202518500379"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.4171\/RLM\/606"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmps.2016.04.033"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2016.07.012"},{"key":"atypb11","first-page":"184","volume":"1","author":"Dal Maso G.","year":"2017","journal-title":"Appl. Math. Res. Express. AMRX"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1007\/s10884-014-9409-7"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1017\/S030821050500079X"},{"key":"atypb14","volume-title":"Pitman","author":"Grisvard P.","year":"1985"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202514500092"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1051\/cocv\/2019006"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1007\/s10884-018-9666-y"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1051\/cocv\/2014004"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1051\/cocv\/2010054"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.4171\/JEMS\/639"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4939-2706-7"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1007\/s10884-015-9461-y"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2017.05.002"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.4171\/IFB\/396"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0207(19990330)44:9<1267::AID-NME486>3.0.CO;2-7"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1007\/s00028-020-00571-4"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2011.01.031"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202517500257"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1137\/12088286X"},{"key":"atypb30","doi-asserted-by":"crossref","first-page":"591","DOI":"10.3934\/dcdss.2013.6.591","volume":"6","author":"Roub\u00ed\u010dek T.","year":"2013","journal-title":"Discrete Contin. Dyn. Syst. Ser. S"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1007\/s00161-009-0106-4"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.1051\/cocv\/2016006"},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.4171\/IFB\/377"},{"key":"atypb34","doi-asserted-by":"publisher","DOI":"10.1017\/S0956792516000097"},{"key":"atypb35","doi-asserted-by":"crossref","DOI":"10.1090\/chel\/343","volume-title":"Navier-Stokes Equations, Theory and Numerical Analysis","author":"Temam R.","year":"2001"},{"key":"atypb36","doi-asserted-by":"crossref","first-page":"1487","DOI":"10.3934\/dcdss.2017077","volume":"10","author":"Thomas M.","year":"2017","journal-title":"Discrete Contin. Dyn. Syst. Ser. S"}],"container-title":["SIAM Journal on Mathematical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/20M1355823","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:47:02Z","timestamp":1787316422000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/20M1355823"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":36,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1137\/20M1355823"],"URL":"https:\/\/doi.org\/10.1137\/20m1355823","relation":{},"ISSN":["0036-1410","1095-7154"],"issn-type":[{"value":"0036-1410","type":"print"},{"value":"1095-7154","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1]]}}}