{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:02:33Z","timestamp":1787320953940,"version":"build-2736575974"},"reference-count":83,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2014,1]]},"abstract":"<jats:p>We present a stability result for a wide class of doubly nonlinear equations, featuring general maximal monotone operators and (possibly) nonconvex and nonsmooth energy functionals. The limit analysis consists in the reformulation of the differential evolution as a scalar energy-conservation equation with the aid of the so-called Fitzpatrick theory for the representation of monotone operators. In particular, our result applies to the vanishing viscosity approximation of rate-independent systems.<\/jats:p>","DOI":"10.1137\/130909391","type":"journal-article","created":{"date-parts":[[2014,3,25]],"date-time":"2014-03-25T10:45:53Z","timestamp":1395744353000},"page":"1071-1107","source":"Crossref","is-referenced-by-count":9,"title":["Stability Results for Doubly Nonlinear Differential Inclusions by Variational Convergence"],"prefix":"10.1137","volume":"52","author":[{"given":"Thomas","family":"Roche","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Riccarda","family":"Rossi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ulisse","family":"Stefanelli","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2014,3,25]]},"reference":[{"key":"atypb1","first-page":"1","volume":"7","author":"Aizicovici S.","year":"1997","journal-title":"Panamer. Math. J."},{"key":"atypb2","first-page":"19","author":"Akagi G.","year":"2008","journal-title":"Tokyo"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1007\/s00028-010-0079-6"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2010.10.019"},{"key":"atypb5","first-page":"683","volume":"14","author":"Akagi G.","year":"2004","journal-title":"Adv. Math. Sci. Appl."},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2010.04.047"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2011.04.014"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2010.12.027"},{"key":"atypb9","first-page":"75","volume":"26","author":"Arai T.","year":"1979","journal-title":"J. Fac. Sci. Univ. Tokyo Sect. IA Math."},{"key":"atypb10","unstructured":"H. Attouch,<i>Variational Convergence for Functions and Operators<\/i> Pitman (Advanced Publishing Program), Boston, MA, 1984."},{"key":"atypb11","doi-asserted-by":"crossref","first-page":"1161","DOI":"10.57262\/die\/1370021920","volume":"6","author":"Auchmuty G.","year":"1993","journal-title":"Differential Integral Equations"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1137\/0322035"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1007\/BF02844536"},{"key":"atypb14","first-page":"207","author":"Ball J. M.","year":"1989","journal-title":"Berlin"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-09-04698-4"},{"key":"atypb16","unstructured":"H. Brezis,<i>Op\u00e9rateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert<\/i> North-Holland Math. Stud. 5, North-Holland, Amsterdam, 1973."},{"key":"atypb17","first-page":"A1197","volume":"282","author":"Brezis H.","year":"1976","journal-title":"C. R. Acad. Sci. Paris S\u00e9r. A-B"},{"key":"atypb18","first-page":"A971","volume":"282","author":"Brezis H.","year":"1976","journal-title":"C. R. Acad. Sci. Paris S\u00e9r. A-B"},{"key":"atypb19","doi-asserted-by":"crossref","unstructured":"M. Brokate and J. Sprekels,<i>Hysteresis and Phase Transitions<\/i> Appl. Math. Sci. 121, Springer, Berlin, 1996.","DOI":"10.1007\/978-1-4612-4048-8"},{"key":"atypb20","first-page":"87","volume":"15","author":"Buliga M.","year":"2008","journal-title":"J. Convex Anal."},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1007\/s10440-009-9488-3"},{"key":"atypb22","doi-asserted-by":"crossref","unstructured":"R. S. Burachik and B. F. Svaiter,<i>Maximal monotone operators, convex functions and a special family of enlargements<\/i>Set-Valued Anal., 10 (2002), pp. 297-316.","DOI":"10.1023\/A:1020639314056"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-03-07053-9"},{"key":"atypb24","doi-asserted-by":"crossref","unstructured":"C. Castaing and M. Valadier,<i>Convex Analysis and Measurable Multifunctions<\/i> Lecture Notes in Math. 580, Springer-Verlag, Berlin, 1977.","DOI":"10.1007\/BFb0087685"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1007\/BF03167565"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1080\/03605309908820706"},{"key":"atypb27","doi-asserted-by":"crossref","unstructured":"G. Dal Maso,<i>An Introduction to $\\Gamma$-Convergence<\/i> Progress in Nonlinear Differential Equations and Their Applications 8, Birkh\u00e4user Boston, Boston, MA, 1993.","DOI":"10.1007\/978-1-4612-0327-8"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-005-0407-0"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-004-0351-4"},{"key":"atypb30","doi-asserted-by":"crossref","unstructured":"J. Diestel and J. J. Uhl, Jr,<i>Vector Measures<\/i> AMS, Providence, RI, 1977.","DOI":"10.1090\/surv\/015"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1002\/mma.1102"},{"key":"atypb32","first-page":"151","volume":"13","author":"Efendiev M. A.","year":"2006","journal-title":"J. Convex Anal."},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2011.02.014"},{"key":"atypb34","first-page":"59","author":"Fitzpatrick S.","year":"1988","journal-title":"Canberra"},{"key":"atypb35","unstructured":"I. Fonseca and G. Leoni,<i>Modern Methods in the Calculus of Variations: $L^p$ Spaces<\/i> Springer Monographs in Mathematics, Springer, New York, 2007."},{"key":"atypb36","doi-asserted-by":"publisher","DOI":"10.1515\/CRELLE.2006.044"},{"key":"atypb37","unstructured":"P. Germain,<i>Cours de m\u00e9canique des milieux continus. TomeI: Th\u00e9orie G\u00e9n\u00e9rale<\/i> Masson et Cie, \u00c9diteurs, Paris, 1973."},{"key":"atypb38","doi-asserted-by":"publisher","DOI":"10.1007\/s11784-008-0083-4"},{"key":"atypb39","unstructured":"N. Ghoussoub,<i>Selfdual Partial Differential Systems and Their Variational Principles<\/i> Springer, New York, 2009."},{"key":"atypb40","unstructured":"W. Han and B. D. Reddy,<i>Plasticity, Mathematical Theory and Numerical Analysis<\/i> Springer, New York, 1999."},{"key":"atypb41","doi-asserted-by":"publisher","DOI":"10.1002\/zamm.201000129"},{"key":"atypb42","first-page":"47","author":"Krej\u010d\u00ed P.","year":"1999","journal-title":"Boca Raton, FL"},{"key":"atypb43","doi-asserted-by":"publisher","DOI":"10.1007\/s00526-004-0267-8"},{"key":"atypb44","first-page":"553","volume":"17","author":"Marques Alves M.","year":"2010","journal-title":"J. Convex Anal."},{"key":"atypb45","doi-asserted-by":"publisher","DOI":"10.1007\/s11228-004-4170-4"},{"issue":"208","key":"atypb46","first-page":"873","volume":"136","author":"Mart\u00ednez-Legaz J. E.","journal-title":"Proc. Amer. Math. Soc."},{"key":"atypb47","doi-asserted-by":"publisher","DOI":"10.1137\/S0036141003429906"},{"key":"atypb48","first-page":"461","author":"Mielke A.","year":"2005","journal-title":"New York"},{"key":"atypb49","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2009.25.585"},{"key":"atypb50","doi-asserted-by":"publisher","DOI":"10.1051\/cocv\/2010054"},{"key":"atypb51","doi-asserted-by":"publisher","DOI":"10.1007\/s00526-011-0482-z"},{"key":"atypb52","doi-asserted-by":"publisher","DOI":"10.1007\/s00032-012-0190-y"},{"key":"atypb53","doi-asserted-by":"publisher","DOI":"10.1142\/S021820250600111X"},{"key":"atypb54","doi-asserted-by":"publisher","DOI":"10.1007\/s00526-007-0119-4"},{"key":"atypb55","doi-asserted-by":"publisher","DOI":"10.1007\/s00030-003-1052-7"},{"key":"atypb56","doi-asserted-by":"publisher","DOI":"10.1007\/s002050200194"},{"key":"atypb57","first-page":"608","volume":"271","author":"Moreau J.-J.","year":"1970","journal-title":"C. R. Acad. Sci. Paris S\u00e9r. II M\u00e9c. Phys. Chim. Sci. Univers Sci. Terre"},{"key":"atypb58","first-page":"A118","volume":"273","author":"Moreau J.-J.","year":"1971","journal-title":"C. R. Acad. Sci. Paris S\u00e9r. A-B"},{"key":"atypb59","first-page":"1","author":"Moreau J.-J.","year":"1988","journal-title":"Basel"},{"key":"atypb60","first-page":"A1035","volume":"282","author":"Nayroles B.","year":"1976","journal-title":"C. R. Acad. Sci. Paris S\u00e9r. A-B"},{"key":"atypb61","first-page":"2","volume":"6","author":"Nayroles B.","year":"1976","journal-title":"Travaux S\u00e9m. Anal. Convexe"},{"key":"atypb62","doi-asserted-by":"publisher","DOI":"10.1017\/S0004972700033748"},{"key":"atypb63","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2004.05.018"},{"key":"atypb64","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2004.03.017"},{"key":"atypb65","doi-asserted-by":"publisher","DOI":"10.1017\/S1446181100009731"},{"key":"atypb66","first-page":"97","volume":"7","author":"Rossi R.","year":"2008","journal-title":"Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)"},{"key":"atypb67","doi-asserted-by":"publisher","DOI":"10.1051\/cocv:2006013"},{"key":"atypb68","first-page":"57","volume":"10","author":"Roub\u00ed\u010dek T.","year":"2000","journal-title":"Adv. Math. Sci. Appl."},{"key":"atypb69","first-page":"61","volume":"56","author":"Schimperna G.","year":"2008","journal-title":"Asymptot. Anal."},{"key":"atypb70","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2007.18.15"},{"key":"atypb71","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2006.14.801"},{"key":"atypb72","first-page":"243","volume":"29","author":"Senba T.","year":"1986","journal-title":"Funkcial. Ekval."},{"key":"atypb73","doi-asserted-by":"publisher","DOI":"10.1137\/070684574"},{"key":"atypb74","doi-asserted-by":"publisher","DOI":"10.1137\/070692571"},{"key":"atypb75","first-page":"81","volume":"140","author":"Stefanelli U.","year":"2009","journal-title":"Istit. Lombardo Accad. Sci. Lett. Rend. A"},{"key":"atypb76","first-page":"71","volume":"16","author":"Stefanelli U.","year":"2009","journal-title":"J. Convex Anal."},{"key":"atypb77","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-03-07083-7"},{"key":"atypb78","doi-asserted-by":"crossref","unstructured":"M. Valadier,<i>Young measures<\/i> in Methods of Nonconvex Analysis (Varenna, 1989), Lecture Notes in Math. 1446, Springer, Berlin, 1990, pp. 152-188.","DOI":"10.1007\/BFb0084935"},{"key":"atypb79","doi-asserted-by":"crossref","unstructured":"A. Visintin,<i>Differential Models of Hysteresis<\/i> Appl. Math. Sci. 111, Springer, Berlin, 1994.","DOI":"10.1007\/978-3-662-11557-2"},{"key":"atypb80","first-page":"633","volume":"18","author":"Visintin A.","year":"2008","journal-title":"Adv. Math. Sci. Appl."},{"key":"atypb81","first-page":"363","volume":"4","author":"Visintin A.","year":"2011","journal-title":"Boll. Unione Mat. Ital. (9)"},{"key":"atypb82","doi-asserted-by":"publisher","DOI":"10.3934\/dcdss.2013.6.257"},{"key":"atypb83","doi-asserted-by":"publisher","DOI":"10.1007\/s00526-012-0519-y"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/130909391","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:01:31Z","timestamp":1787317291000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/130909391"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1]]},"references-count":83,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2014,1]]}},"alternative-id":["10.1137\/130909391"],"URL":"https:\/\/doi.org\/10.1137\/130909391","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,1]]}}}