{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,26]],"date-time":"2026-09-26T01:22:28Z","timestamp":1790385748973,"version":"4.1.0"},"reference-count":37,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"name":"BASAL","award":["AFB-170001"],"award-info":[{"award-number":["AFB-170001"]}]},{"DOI":"10.13039\/501100002850","name":"Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["1171854"],"award-info":[{"award-number":["1171854"]}],"id":[{"id":"10.13039\/501100002850","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003329","name":"Ministerio de Econom\u00eda y Competitividad","doi-asserted-by":"publisher","award":["MTM2014-59179-C2-1-P"],"award-info":[{"award-number":["MTM2014-59179-C2-1-P"]}],"id":[{"id":"10.13039\/501100003329","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>We disclose an interesting connection between the gradient flow of a $\\mathscr{C}^2$-smooth function $\\psi$ and strongly evanescent orbits of the second-order gradient system defined by the square-norm of $\\nabla\\psi$, under an adequate convexity assumption. As a consequence, we obtain the following surprising result for two $\\mathscr{C}^2$, convex, and bounded from below functions $\\psi_1$, $\\psi_2$: if $||\\nabla\\psi_1||=||\\nabla\\psi_2||$, then $\\psi_1=\\psi_2 + k$ for some $k\\in \\mathbb{R}$.<\/jats:p>","DOI":"10.1137\/16m1153418","type":"journal-article","created":{"date-parts":[[2018,7,19]],"date-time":"2018-07-19T14:43:14Z","timestamp":1532011394000},"page":"2049-2066","source":"Crossref","is-referenced-by-count":10,"title":["Gradient Flows, Second-Order Gradient Systems and Convexity"],"prefix":"10.1137","volume":"28","author":[{"given":"Tahar Z.","family":"Boulmezaoud","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Philippe","family":"Cieutat","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Aris","family":"Daniilidis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,7,19]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1137\/040605266"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012902419977"},{"key":"atypb3","doi-asserted-by":"crossref","unstructured":"H. Attouch, G. Buttazzo, and G. Michaille,\n                      Variational Analysis in Sobolev and BV Spaces: Applications to PDEs and Optimization\n                      , MOS-SIAM Ser. Optim. 17, 2nd ed., SIAM, Philadelphia, PA, 2014.","DOI":"10.1137\/1.9781611973488"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1137\/130910294"},{"key":"atypb5","first-page":"45","author":"Auchmuty G.","year":"2007","journal-title":"RI"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1023\/A:1014460029093"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1016\/0022-1236(78)90093-9"},{"key":"atypb8","unstructured":"G. Barles,\n                      Solutions de viscosite\u0301 des e\u0301quations de Hamilton-Jacobi\n                      , Math. Appl. 17, Springer, Paris, 1994."},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1080\/03605300500361461"},{"key":"atypb10","unstructured":"G. Barles, O. Ley, T.T. Nguyen, and T. Phan,\n                      Large Time Behavior of Unbounded Solutions of First-Order Hamilton-Jacobi Equations in $\\R^n$\n                      , preprint, arXiv:1709.08387, 2017."},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1287\/moor.2016.0817"},{"key":"atypb12","unstructured":"H. Bre\u0301zis,\n                      Ope\u0301rateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert\n                      , North-Holland Math. Stud. 5, American Elsevier, New York, 1973."},{"key":"atypb13","first-page":"A971","volume":"282","author":"Bre\u0301zis H.","year":"1976","journal-title":"C. R. Acad. Sci. Paris Se\u0301r. A--B"},{"key":"atypb14","first-page":"A1197","volume":"282","author":"Bre\u0301zis H.","year":"1976","journal-title":"C. R. Acad. Sci. Paris Se\u0301r. A--B"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1142\/S0219530509001438"},{"key":"atypb16","first-page":"183","volume":"252","author":"Crandall M. G.","year":"1981","journal-title":"C. R. Math. Acad. Sci. Paris"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1006\/jfan.1994.1119"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1016\/j.matpur.2010.03.007"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1007\/s12220-013-9464-z"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(74)90025-0"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1007\/s00030-007-2047-6"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1007\/s00208-004-0558-6"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1007\/BF00944741"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2011.01.012"},{"key":"atypb25","unstructured":"S.Z. Huang,\n                      Gradient Inequalities: With Applications to Asymptotic Behavior and Stability of Gradient-Like Systems\n                      , Math. Surveys Monogr. 126, American Mathematical Society, Providence, RI, 2006."},{"key":"atypb26","unstructured":"H. Ishii,\n                      Asymptotic solutions of Hamilton-Jacobi equations for large time and related topics\n                      , in ICIAM 07: 6th International Congress on Industrial and Applied Mathematics, European Mathematical Society, Zurich, 2009, pp. 193-217."},{"key":"atypb27","first-page":"450","volume":"98","author":"Kruz\u030ckov S. N.","year":"1975","journal-title":"S.)"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.5802\/aif.1638"},{"key":"atypb29","unstructured":"P. L. Lions, G. Papanicolau, and S. R. S. Varadhan,\n                      Homogenization of Hamilton-Jacobi Equation\n                      , preprint,http:\/\/localwww.math.unipd.it\/~bardi\/didattica\/Nonlinear_PDE_%20homogenization_Dott_%202011\/LPV87.pdf, 1987."},{"key":"atypb30","unstructured":"P. L. Lions,\n                      Generalized Solutions of Hamilton-Jacobi Equations\n                      , Res. Notes Math. 69, Pitman, Boston, MA, 1982."},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1007\/BF00181220"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.1080\/03605309908821451"},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1967-11761-0"},{"key":"atypb34","doi-asserted-by":"crossref","unstructured":"J. Palis and W. De Melo,\n                      Geometric Theory of Dynamical Systems: An Introduction\n                      , Springer, New York, 1982 (in Portuguese).","DOI":"10.1007\/978-1-4612-5703-5"},{"key":"atypb35","unstructured":"R. Phelps,\n                      Convex Functions, Monotone Operators and Differentiability\n                      , Lecture Notes in Math. 1364, 2nd ed., Springer, Berlin, 1993."},{"key":"atypb36","unstructured":"T. Rockafellar,\n                      Convex Analysis\n                      , Princeton University Press, Princeton, NJ, 1997."},{"key":"atypb37","doi-asserted-by":"publisher","DOI":"10.5802\/aif.1648"}],"container-title":["SIAM Journal on Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/16M1153418","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:18:47Z","timestamp":1787339927000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/16M1153418"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1]]},"references-count":37,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["10.1137\/16M1153418"],"URL":"https:\/\/doi.org\/10.1137\/16m1153418","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1]]}}}