{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T12:54:50Z","timestamp":1740142490777,"version":"3.37.3"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2021,3,18]],"date-time":"2021-03-18T00:00:00Z","timestamp":1616025600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,3,18]],"date-time":"2021-03-18T00:00:00Z","timestamp":1616025600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2021,4]]},"DOI":"10.1007\/s40314-021-01459-w","type":"journal-article","created":{"date-parts":[[2021,3,18]],"date-time":"2021-03-18T19:12:58Z","timestamp":1616094778000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["New general stability for a variable coefficient thermo-viscoelastic-coupled system of second sound with acoustic boundary conditions"],"prefix":"10.1007","volume":"40","author":[{"given":"Abdelaziz","family":"Limam","sequence":"first","affiliation":[]},{"given":"Yamna","family":"Boukhatem","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4051-4711","authenticated-orcid":false,"given":"Benyattou","family":"Benabderrahmane","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,3,18]]},"reference":[{"issue":"15","key":"1459_CR1","doi-asserted-by":"publisher","first-page":"867","DOI":"10.1016\/j.crma.2009.05.011","volume":"347","author":"F Alabau-Boussouira","year":"2009","unstructured":"Alabau-Boussouira F, Cannarsa P (2009) A general method for proving sharp energy decay rates for memory-dissipative evolution equations. Compt Rend Math 347(15):867\u2013872","journal-title":"Compt Rend Math"},{"key":"1459_CR2","volume-title":"Mathematical methods of classical mechanics","author":"VI Arnold","year":"2013","unstructured":"Arnold VI (2013) Mathematical methods of classical mechanics, vol 60. Springer, Berlin"},{"issue":"10","key":"1459_CR3","doi-asserted-by":"publisher","first-page":"1057","DOI":"10.1016\/S0021-7824(00)00173-2","volume":"79","author":"G Avalos","year":"2000","unstructured":"Avalos G, Lasiecka I, Rebarber R (2000) Uniform decay properties of a model in structural acoustics. J Math Pures Appl 79(10):1057\u20131072","journal-title":"J Math Pures Appl"},{"issue":"9","key":"1459_CR4","doi-asserted-by":"publisher","first-page":"895","DOI":"10.1512\/iumj.1976.25.25071","volume":"25","author":"JT Beale","year":"1976","unstructured":"Beale JT (1976) Spectral properties of an acoustic boundary condition. Indiana Univ Math J 25(9):895\u2013917","journal-title":"Indiana Univ Math J"},{"issue":"6","key":"1459_CR5","doi-asserted-by":"publisher","first-page":"1276","DOI":"10.1090\/S0002-9904-1974-13714-6","volume":"80","author":"JT Beale","year":"1974","unstructured":"Beale JT, Rosencrans SI (1974) Acoustic boundary conditions. Bull Am Math Soc 80(6):1276\u20131279","journal-title":"Bull Am Math Soc"},{"key":"1459_CR6","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1016\/j.na.2013.11.019","volume":"97","author":"Y Boukhatem","year":"2014","unstructured":"Boukhatem Y, Benabderrahmane B (2014) Existence and decay of solutions for a viscoelastic wave equation with acoustic boundary conditions. Nonlinear Anal TMA 97:191\u2013209","journal-title":"Nonlinear Anal TMA"},{"key":"1459_CR7","first-page":"1","volume":"20","author":"Y Boukhatem","year":"2018","unstructured":"Boukhatem Y, Benabderrahmane B (2018) Asymptotic behavior for a past history viscoelastic problem with acoustic boundary conditions. Appl Anal 20:1\u201321","journal-title":"Appl Anal"},{"key":"1459_CR8","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/1687-1847-2014-1","volume":"2014","author":"F Boulanouar","year":"2014","unstructured":"Boulanouar F, Drabla S (2014) General boundary stabilization result of memory-type thermoelasticity with second sound. Electron J Differ Equ 2014:1\u201318","journal-title":"Electron J Differ Equ"},{"issue":"1","key":"1459_CR9","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1007\/s40314-015-0236-1","volume":"36","author":"P Braz e Silva","year":"2017","unstructured":"Braz e Silva P, Clark HR, Frota CL (2017) On a nonlinear coupled system of thermoelastic type with acoustic boundary conditions. Comp Appl Math 36(1):397\u2013414","journal-title":"Comp Appl Math"},{"key":"1459_CR10","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1016\/j.nonrwa.2014.09.016","volume":"22","author":"MM Cavalcanti","year":"2015","unstructured":"Cavalcanti MM, Cavalcanti ADD, Lasiecka I, Wang X (2015) Existence and sharp decay rate estimates for a von Karman system with long memory. Nonlinear Anal RWA 22:289\u2013306","journal-title":"Nonlinear Anal RWA"},{"key":"1459_CR11","first-page":"297","volume":"66","author":"CL Frota","year":"2005","unstructured":"Frota CL, Larkin NA (2005) Uniform stabilization for a hyperbolic equation with acoustic boundary conditions in simple connected domains. Prog Nonlinear Differ Equ Appl 66:297\u2013312","journal-title":"Prog Nonlinear Differ Equ Appl"},{"issue":"2","key":"1459_CR12","doi-asserted-by":"publisher","first-page":"748","DOI":"10.1016\/j.jmaa.2011.04.079","volume":"382","author":"A Guesmia","year":"2011","unstructured":"Guesmia A (2011) Asymptotic stability of abstract dissipative systems with infinite memory. J Math Anal Appl 382(2):748\u2013760","journal-title":"J Math Anal Appl"},{"issue":"1","key":"1459_CR13","doi-asserted-by":"publisher","first-page":"6","DOI":"10.1007\/s00033-017-0897-2","volume":"69","author":"T Hamadouche","year":"2018","unstructured":"Hamadouche T, Messaoudi SA (2018) Existence and energy decay of a nonuniform Timoshenko system with second sound. Z Angew Math Phys 69(1):6","journal-title":"Z Angew Math Phys"},{"issue":"3","key":"1459_CR14","doi-asserted-by":"publisher","first-page":"346","DOI":"10.1002\/mma.1041","volume":"32","author":"X Han","year":"2009","unstructured":"Han X, Wang M (2009) General decay of energy for a viscoelastic equation with nonlinear damping. Math Methods Appl Sci 32(3):346\u2013358","journal-title":"Math Methods Appl Sci"},{"issue":"3","key":"1459_CR15","first-page":"507","volume":"6","author":"I Lasiecka","year":"1993","unstructured":"Lasiecka I, Tataru D (1993) Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping. Differ Integ Equ 6(3):507\u2013533","journal-title":"Differ Integ Equ"},{"issue":"3","key":"1459_CR16","doi-asserted-by":"publisher","first-page":"031504","DOI":"10.1063\/1.4793988","volume":"54","author":"I Lasiecka","year":"2013","unstructured":"Lasiecka I, Messaoudi SA, Mustafa MI (2013) Note on intrinsic decay rates for abstract wave equations with memory. J Math Phys 54(3):031504","journal-title":"J Math Phys"},{"key":"1459_CR17","volume-title":"Semigroups associated with dissipative systems","author":"Z Liu","year":"1999","unstructured":"Liu Z, Zheng S (1999) Semigroups associated with dissipative systems, vol 398. CRC Press, Boca Raton"},{"issue":"5","key":"1459_CR18","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1016\/0022-5096(67)90024-5","volume":"15","author":"HW Lord","year":"1967","unstructured":"Lord HW, Shulman Y (1967) A generalized dynamical theory of thermoelasticity. J Mech Phys Solids 15(5):299\u2013309","journal-title":"J Mech Phys Solids"},{"issue":"2","key":"1459_CR19","doi-asserted-by":"publisher","first-page":"1457","DOI":"10.1016\/j.jmaa.2007.11.048","volume":"341","author":"SA Messaoudi","year":"2008","unstructured":"Messaoudi SA (2008) General decay of solutions of a viscoelastic equation. J Math Anal Appl 341(2):1457\u20131467","journal-title":"J Math Anal Appl"},{"issue":"2","key":"1459_CR20","first-page":"413","volume":"51","author":"SA Messaoudi","year":"2018","unstructured":"Messaoudi SA, Al-Khulaifi W (2018) General and optimal decay for a viscoelastic equation with boundary feedback. Topol Methods Nonlinear Anal 51(2):413\u2013427","journal-title":"Topol Methods Nonlinear Anal"},{"key":"1459_CR21","volume-title":"Theoretical acoustics","author":"PM Morse","year":"1968","unstructured":"Morse PM, Ingard KU (1968) Theoretical acoustics. Princeton University Press, Princeton"},{"issue":"4","key":"1459_CR22","doi-asserted-by":"publisher","first-page":"777","DOI":"10.1007\/s00033-011-0190-8","volume":"63","author":"MI Mustafa","year":"2012","unstructured":"Mustafa MI (2012) Boundary stabilization of memory-type thermoelasticity with second sound. Z Angew Math Phys 63(4):777\u2013792","journal-title":"Z Angew Math Phys"},{"issue":"1","key":"1459_CR23","doi-asserted-by":"publisher","first-page":"192","DOI":"10.1002\/mma.4604","volume":"41","author":"MI Mustafa","year":"2018","unstructured":"Mustafa MI (2018) Optimal decay rates for the viscoelastic wave equation. Math Methods Appl Sci 41(1):192\u2013204","journal-title":"Math Methods Appl Sci"},{"issue":"2","key":"1459_CR24","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1007\/s10883-018-9410-2","volume":"25","author":"MI Mustafa","year":"2019","unstructured":"Mustafa MI (2019) Asymptotic stability for the second order evolution equation with memory. J Dyn Control Syst 25(2):263\u2013273","journal-title":"J Dyn Control Syst"},{"issue":"5","key":"1459_CR25","doi-asserted-by":"publisher","first-page":"053702","DOI":"10.1063\/1.4711830","volume":"53","author":"MI Mustafa","year":"2012","unstructured":"Mustafa MI, Messaoudi SA (2012) General stability result for viscoelastic wave equations. J Math Phys 53(5):053702","journal-title":"J Math Phys"},{"issue":"8","key":"1459_CR26","doi-asserted-by":"publisher","first-page":"083505","DOI":"10.1063\/1.3187780","volume":"50","author":"JY Park","year":"2009","unstructured":"Park JY, Park SH (2009) General decay for quasilinear viscoelastic equations with nonlinear weak damping. J Math Phys 50(8):083505","journal-title":"J Math Phys"},{"issue":"3","key":"1459_CR27","doi-asserted-by":"publisher","first-page":"993","DOI":"10.1016\/j.na.2010.09.057","volume":"74","author":"JY Park","year":"2011","unstructured":"Park JY, Park SH (2011) Decay rate estimates for wave equations of memory type with acoustic boundary conditions. Nonlinear Anal TMA 74(3):993\u2013998","journal-title":"Nonlinear Anal TMA"},{"issue":"5","key":"1459_CR28","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1002\/mma.298","volume":"25","author":"R Racke","year":"2002","unstructured":"Racke R (2002) Thermoelasticity with second sound-exponential stability in linear and non-linear 1-d. Math Methods Appl Sci 25(5):409\u2013441","journal-title":"Math Methods Appl Sci"},{"issue":"2","key":"1459_CR29","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1090\/qam\/1976372","volume":"61","author":"R Racke","year":"2003","unstructured":"Racke R (2003) Asymptotic behavior of solutions in linear 2- or 3-D thermoelasticity with second sound. Quart Appl Math 61(2):315\u2013328","journal-title":"Quart Appl Math"},{"issue":"4","key":"1459_CR30","doi-asserted-by":"publisher","first-page":"727","DOI":"10.1090\/qam\/1193663","volume":"50","author":"MA Tarabek","year":"1992","unstructured":"Tarabek MA (1992) On the existence of smooth solutions in one-dimensional nonlinear thermoelasticity with second sound. Quart Appl Math 50(4):727\u2013742","journal-title":"Quart Appl Math"},{"issue":"1","key":"1459_CR31","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1186\/1687-2770-2011-55","volume":"2011","author":"ST Wu","year":"2011","unstructured":"Wu ST (2011) General decay for a wave equation of Kirchhoff type with a boundary control of memory type. Bound Value Probl 2011(1):55","journal-title":"Bound Value Probl"},{"issue":"4","key":"1459_CR32","first-page":"291","volume":"74","author":"E Zuazua","year":"1995","unstructured":"Zuazua E (1995) Controllability of the linear system of thermoelasticity. J Math Pures Appl 74(4):291\u2013316","journal-title":"J Math Pures Appl"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-021-01459-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s40314-021-01459-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-021-01459-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,8]],"date-time":"2021-04-08T22:03:45Z","timestamp":1617919425000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s40314-021-01459-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,18]]},"references-count":32,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,4]]}},"alternative-id":["1459"],"URL":"https:\/\/doi.org\/10.1007\/s40314-021-01459-w","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"type":"print","value":"2238-3603"},{"type":"electronic","value":"1807-0302"}],"subject":[],"published":{"date-parts":[[2021,3,18]]},"assertion":[{"value":"25 February 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 February 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 February 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 March 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"88"}}