{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T05:49:24Z","timestamp":1774417764425,"version":"3.50.1"},"reference-count":37,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2018,10,9]],"date-time":"2018-10-09T00:00:00Z","timestamp":1539043200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,1,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This paper considers a general framework for the study of the existence of\nquasi-variational and variational solutions to a class of nonlinear evolution\nsystems in convex sets of Banach spaces describing constraints on a\nlinear combination of partial derivatives of the solutions. The quasi-linear operators are\nof monotone type, but are not required to be coercive for the existence of weak solutions, which\nis obtained by a double penalization\/regularization for the approximation of the solutions. In\nthe case of time-dependent convex sets that are independent of the solution, we show\nalso the uniqueness and the continuous dependence of the strong solutions of the variational\ninequalities, extending previous results to a more general framework.<\/jats:p>","DOI":"10.1515\/anona-2018-0113","type":"journal-article","created":{"date-parts":[[2019,2,18]],"date-time":"2019-02-18T09:53:23Z","timestamp":1550483603000},"page":"250-277","source":"Crossref","is-referenced-by-count":19,"title":["Evolutionary quasi-variational and variational inequalities with constraints on the derivatives"],"prefix":"10.1515","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7624-4816","authenticated-orcid":false,"given":"Fernando","family":"Miranda","sequence":"first","affiliation":[{"name":"CMAT \u2013 Departamento de Matem\u00e1tica , Escola de Ci\u00eancias , Universidade do Minho , Campus de Gualtar, 4710-057 Braga , Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8438-0749","authenticated-orcid":false,"given":"Jos\u00e9 Francisco","family":"Rodrigues","sequence":"additional","affiliation":[{"name":"CMAFcIO \u2013 Departamento de Matem\u00e1tica , Faculdade de Ci\u00eancias , Universidade de Lisboa , P-1749-016 Lisboa , Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0286-1616","authenticated-orcid":false,"given":"Lisa","family":"Santos","sequence":"additional","affiliation":[{"name":"CMAT \u2013 Departamento de Matem\u00e1tica , Escola de Ci\u00eancias , Universidade do Minho , Campus de Gualtar, 4710-057 Braga , Portugal"}]}],"member":"374","published-online":{"date-parts":[[2018,10,9]]},"reference":[{"key":"2021020917364184095_j_anona-2018-0113_ref_001","unstructured":"C.  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Part II 30 (1981), 1\u201387."},{"key":"2021020917364184095_j_anona-2018-0113_ref_018","unstructured":"N.  Kenmochi,\nParabolic quasi-variational diffusion problems with gradient constraints,\nDiscrete Contin. Dyn. Syst. Ser. S 6 (2013), no. 2, 423\u2013438."},{"key":"2021020917364184095_j_anona-2018-0113_ref_019","unstructured":"N.  Kenmochi and M.  Niezg\u00f3dka,\nWeak solvability for parabolic variational inclusions and application to quasi-variational problems,\nAdv. Math. Sci. Appl. 25 (2016), no. 1, 63\u201398."},{"key":"2021020917364184095_j_anona-2018-0113_ref_020","unstructured":"M.  Kubo,\nQuasi-variational analysis,\nSugaku Expositions 30 (2017), no. 1, 17\u201334."},{"key":"2021020917364184095_j_anona-2018-0113_ref_021","unstructured":"M.  Kunze and J. F.  Rodrigues,\nAn elliptic quasi-variational inequality with gradient constraints and some of its applications,\nMath. Methods Appl. Sci. 23 (2000), no. 10, 897\u2013908."},{"key":"2021020917364184095_j_anona-2018-0113_ref_022","unstructured":"O. A.  Lady\u017eenskaja, V. A.  Solonnikov and N. N.  Ural\u2019ceva,\nLinear and Quasilinear Equations of Parabolic Type,\nTransl. Math. Monogr. 23,\nAmerican Mathematical Society, Providence, 1968."},{"key":"2021020917364184095_j_anona-2018-0113_ref_023","unstructured":"J.-L.  Lions,\nQuelques m\u00e9thodes de r\u00e9solution des probl\u00e8mes aux limites non lin\u00e9aires,\nDunod, Paris, 1969."},{"key":"2021020917364184095_j_anona-2018-0113_ref_024","doi-asserted-by":"crossref","unstructured":"J.-L.  Lions and G.  Stampacchia,\nVariational inequalities,\nComm. Pure Appl. Math. 20 (1967), 493\u2013519.","DOI":"10.1002\/cpa.3160200302"},{"key":"2021020917364184095_j_anona-2018-0113_ref_025","unstructured":"F.  Mignot and J.-P.  Puel,\nIn\u00e9quations d\u2019\u00e9volution paraboliques avec convexes d\u00e9pendant du temps. Applications aux in\u00e9quations quasi variationnelles d\u2019\u00e9volution,\nArch. Ration. Mech. Anal. 64 (1977), no. 1, 59\u201391."},{"key":"2021020917364184095_j_anona-2018-0113_ref_026","doi-asserted-by":"crossref","unstructured":"F.  Miranda and J. F.  Rodrigues,\nOn a variational inequality for incompressible non-Newtonian thick flows,\nRecent Advances in Partial Differential Equations and Applications,\nContemp. Math. 666,\nAmerican Mathematical Society, Providence (2016), 305\u2013316.","DOI":"10.1090\/conm\/666\/13247"},{"key":"2021020917364184095_j_anona-2018-0113_ref_027","unstructured":"F.  Miranda, J.-F.  Rodrigues and L.  Santos,\nOn a p-curl system arising in electromagnetism,\nDiscrete Contin. Dyn. Syst. Ser. S 5 (2012), no. 3, 605\u2013629."},{"key":"2021020917364184095_j_anona-2018-0113_ref_028","unstructured":"L.  Prigozhin,\nOn the Bean critical-state model in superconductivity,\nEuropean J. Appl. Math. 7 (1996), no. 3, 237\u2013247."},{"key":"2021020917364184095_j_anona-2018-0113_ref_029","unstructured":"L.  Prigozhin,\nVariational model of sandpile growth,\nEuropean J. Appl. Math. 7 (1996), no. 3, 225\u2013235."},{"key":"#cr-split#-2021020917364184095_j_anona-2018-0113_ref_030.1","unstructured":"J.-F. Rodrigues, On the mathematical analysis of thick fluids, J. Math. Sci. (N.Y.) 210 (2015), no. 6, 835-848"},{"key":"#cr-split#-2021020917364184095_j_anona-2018-0113_ref_030.2","unstructured":"also published in Zap. Nauchn. Sem. POMI 425 (2014), 117-136."},{"key":"2021020917364184095_j_anona-2018-0113_ref_031","unstructured":"J. F.  Rodrigues and L.  Santos,\nA parabolic quasi-variational inequality arising in a superconductivity model,\nAnn. Sc. Norm. Sup\u00e9r. Pisa Cl. Sci. (4) 29 (2000), no. 1, 153\u2013169."},{"key":"2021020917364184095_j_anona-2018-0113_ref_032","unstructured":"J. F.  Rodrigues and L.  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Differential Equations 229 (2006), no. 1, 204\u2013228."}],"container-title":["Advances in Nonlinear Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/anona\/9\/1\/article-p250.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/anona-2018-0113\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/anona-2018-0113\/html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,27]],"date-time":"2021-02-27T22:23:42Z","timestamp":1614464622000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/anona-2018-0113\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10,9]]},"references-count":37,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2018,10,9]]},"published-print":{"date-parts":[[2020,1,1]]}},"alternative-id":["10.1515\/anona-2018-0113"],"URL":"https:\/\/doi.org\/10.1515\/anona-2018-0113","relation":{},"ISSN":["2191-950X"],"issn-type":[{"value":"2191-950X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,10,9]]}}}