{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:54:51Z","timestamp":1777449291436,"version":"3.51.4"},"reference-count":23,"publisher":"SAGE Publications","issue":"3-4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["ASY"],"published-print":{"date-parts":[[2015,11,9]]},"DOI":"10.3233\/asy-151322","type":"journal-article","created":{"date-parts":[[2015,11,10]],"date-time":"2015-11-10T11:36:11Z","timestamp":1447155371000},"page":"243-278","source":"Crossref","is-referenced-by-count":1,"title":["Homogenization results for a deterministic multi-domains periodic control problem"],"prefix":"10.1177","volume":"95","author":[{"given":"Guy","family":"Barles","sequence":"first","affiliation":[{"name":"Laboratoire de Math\u00e9matiques et Physique Th\u00e9orique (UMR CNRS 7350), F\u00e9d\u00e9ration Denis Poisson (FR CNRS 2964), Universit\u00e9 Fran\u00e7ois Rabelais, Tours, France. E-mails:\u00a0Guy.Barles@lmpt.univ-tours.fr,\u00a0ariela.briani@lmpt.univ-tours.fr,\u00a0Emmanuel.Chasseigne@lmpt.univ-tours.fr"}]},{"given":"Ariela","family":"Briani","sequence":"additional","affiliation":[{"name":"Laboratoire de Math\u00e9matiques et Physique Th\u00e9orique (UMR CNRS 7350), F\u00e9d\u00e9ration Denis Poisson (FR CNRS 2964), Universit\u00e9 Fran\u00e7ois Rabelais, Tours, France. E-mails:\u00a0Guy.Barles@lmpt.univ-tours.fr,\u00a0ariela.briani@lmpt.univ-tours.fr,\u00a0Emmanuel.Chasseigne@lmpt.univ-tours.fr"}]},{"given":"Emmanuel","family":"Chasseigne","sequence":"additional","affiliation":[{"name":"Laboratoire de Math\u00e9matiques et Physique Th\u00e9orique (UMR CNRS 7350), F\u00e9d\u00e9ration Denis Poisson (FR CNRS 2964), Universit\u00e9 Fran\u00e7ois Rabelais, Tours, France. E-mails:\u00a0Guy.Barles@lmpt.univ-tours.fr,\u00a0ariela.briani@lmpt.univ-tours.fr,\u00a0Emmanuel.Chasseigne@lmpt.univ-tours.fr"}]},{"given":"Nicoletta","family":"Tchou","sequence":"additional","affiliation":[{"name":"IRMAR, UMR 6625, Universit\u00e9 de Rennes 1, Rennes, France. E-mail:\u00a0nicoletta.tchou@univ-rennes1.fr"}]}],"member":"179","reference":[{"issue":"3","key":"10.3233\/ASY-151322_ref1","doi-asserted-by":"publisher","first-page":"413","DOI":"10.1007\/s00030-012-0158-1","article-title":"Hamilton\u2013Jacobi equations constrained on networks","volume":"20","author":"Achdou","year":"2012","journal-title":"Nonlinear Differential Equations and Applications"},{"issue":"4","key":"10.3233\/ASY-151322_ref2","doi-asserted-by":"crossref","first-page":"1159","DOI":"10.1137\/S0363012900366741","article-title":"Viscosity solutions methods for singular perturbations in deterministic and stochastic control","volume":"40","author":"Alvarez","year":"2002","journal-title":"SIAM J. Control Optim."},{"issue":"1","key":"10.3233\/ASY-151322_ref3","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1007\/s00205-003-0266-5","article-title":"Singular perturbations of nonlinear degenerate parabolic PDEs: A general convergence result","volume":"170","author":"Alvarez","year":"2003","journal-title":"Arch. Ration. Mech. Anal."},{"key":"10.3233\/ASY-151322_ref4","unstructured":"[4]J.-P.\u00a0Aubin and H.\u00a0Frankowska, Set-Valued Analysis. Systems & Control: Foundations & Applications, Vol.\u00a02, Birkh\u00e4user, Boston, MA, 1990."},{"key":"10.3233\/ASY-151322_ref5","doi-asserted-by":"crossref","unstructured":"[5]M.\u00a0Bardi and I.\u00a0Capuzzo Dolcetta, Optimal Control and Viscosity Solutions of Hamilton\u2013Jacobi\u2013Bellman Equations, Systems & Control: Foundations & Applications, Birkh\u00e4user, Boston, MA, 1997.","DOI":"10.1007\/978-0-8176-4755-1"},{"key":"10.3233\/ASY-151322_ref6","unstructured":"[6]G.\u00a0Barles, Solutions de viscosit\u00e9 des \u00e9quations de Hamilton\u2013Jacobi, Springer, Paris, 1994."},{"issue":"1","key":"10.3233\/ASY-151322_ref7","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/j.na.2010.02.009","article-title":"A short proof of the C 0 , \u03b1 -regularity of viscosity subsolutions for superquadratic viscous Hamilton\u2013Jacobi equations and applications","volume":"73","author":"Barles","year":"2010","journal-title":"Nonlinear Anal."},{"key":"10.3233\/ASY-151322_ref8","unstructured":"[8]G.\u00a0Barles, First order Hamilton\u2013Jacobi equations and applications, in: Hamilton\u2013Jacobi Equations: Approximations, Numerical Analysis and Applications, Lecture Notes in Mathematics, Vol.\u00a02074, Springer, 2011, pp.\u00a049\u2013110."},{"issue":"3","key":"10.3233\/ASY-151322_ref9","first-page":"710","article-title":"A Bellman approach for two-domains optimal control problems in R N","volume":"19","author":"Barles","year":"2013","journal-title":"ESAIM: Control, Optimisation and Calculus of Variations"},{"key":"10.3233\/ASY-151322_ref10","doi-asserted-by":"crossref","first-page":"1712","DOI":"10.1137\/130922288","article-title":"A Bellman approach for regional optimal control problems in R N","volume":"52","author":"Barles","year":"2014","journal-title":"SIAM J. Control Optim."},{"issue":"5","key":"10.3233\/ASY-151322_ref11","doi-asserted-by":"crossref","first-page":"2355","DOI":"10.1512\/iumj.2008.57.3363","article-title":"Ergodic problems and periodic homogenization for fully nonlinear equations in half-space type domains with Neumann boundary conditions","volume":"57","author":"Barles","year":"2008","journal-title":"Indiana Univ. Math. J."},{"issue":"4","key":"10.3233\/ASY-151322_ref12","doi-asserted-by":"crossref","first-page":"1095","DOI":"10.1512\/iumj.1996.45.1145","article-title":"Periodic homogenization of Hamilton\u2013Jacobi equations: Additive eigenvalues and variational formula","volume":"45","author":"Concordel","year":"1996","journal-title":"Indiana Univ. Math. J."},{"issue":"4","key":"10.3233\/ASY-151322_ref13","doi-asserted-by":"crossref","first-page":"665","DOI":"10.1017\/S0308210500023763","article-title":"Periodic homogenization of Hamilton\u2013Jacobi equations: II: Eikonal equations","volume":"127","author":"Concordel","year":"1997","journal-title":"Proc. R. Soc. Edinb., Sect. A"},{"key":"10.3233\/ASY-151322_ref14","doi-asserted-by":"crossref","first-page":"1043","DOI":"10.1016\/S0764-4442(97)87883-4","article-title":"Th\u00e9or\u00e8me KAM faible et th\u00e9orie de Mather sur les syst\u00e8mes lagrangiens","volume":"324","author":"Fathi","year":"1997","journal-title":"C. R. Acad. Sci., Paris, S\u00e9r. I"},{"issue":"6","key":"10.3233\/ASY-151322_ref15","doi-asserted-by":"crossref","first-page":"649","DOI":"10.1016\/S0764-4442(97)84777-5","article-title":"Solutions KAM faibles conjugu\u00e9es et barri\u00e8res de Peierls","volume":"325","author":"Fathi","year":"1997","journal-title":"C. R. Acad. Sci., Paris, S\u00e9r. I, Math."},{"issue":"3","key":"10.3233\/ASY-151322_ref16","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1016\/S0764-4442(98)80144-4","article-title":"Sur la convergence du semi-groupe de Lax\u2013Oleinik","volume":"327","author":"Fathi","year":"1998","journal-title":"C. R. Acad. Sci., Paris, S\u00e9r. I, Math."},{"key":"10.3233\/ASY-151322_ref17","first-page":"99","article-title":"Differential equations with discontinuous right-hand side","volume":"51","author":"Filippov","year":"1960","journal-title":"Matematicheskii Sbornik"},{"issue":"1","key":"10.3233\/ASY-151322_ref20","first-page":"129","article-title":"A Hamilton\u2013Jacobi approach to junction problems and applications to traffic flows","volume":"19","author":"Imbert","year":"2013","journal-title":"ESAIM: Control, Optimisation and Calculus of Variations"},{"key":"10.3233\/ASY-151322_ref21","first-page":"33","article-title":"Hamilton\u2013Jacobi equations with discontinuous Hamiltonians on arbitrary open sets","volume":"28","author":"Ishii","year":"1985","journal-title":"Bull. Faculty Sci. Eng. Chuo Univ."},{"key":"10.3233\/ASY-151322_ref22","doi-asserted-by":"crossref","unstructured":"[22]H.\u00a0Ishii, A short introduction to viscosity solutions and the large time behavior of solutions of Hamilton\u2013Jacobi equations, in: Hamilton\u2013Jacobi Equations: Approximations, Numerical Analysis and Applications, Lecture Notes in Mathematics, Vol.\u00a02074, Springer, 2011, pp.\u00a0111\u2013250.","DOI":"10.1007\/978-3-642-36433-4_3"},{"key":"10.3233\/ASY-151322_ref23","unstructured":"[23]P.L.\u00a0Lions, Generalized Solutions of Hamilton\u2013Jacobi Equations, Research Notes in Mathematics, Vol.\u00a069, Pitman, Boston, MA, 1982."},{"key":"10.3233\/ASY-151322_ref25","doi-asserted-by":"crossref","first-page":"449","DOI":"10.4171\/IFB\/29","article-title":"The \u201chump\u201d effect in solid propellant combustion","volume":"2","author":"Namah","year":"2000","journal-title":"Interfaces Free Bound"},{"key":"10.3233\/ASY-151322_ref26","first-page":"151","article-title":"Syst\u00e8mes de commande et \u00e9quation au contingent","volume":"9","author":"Wasewski","year":"1961","journal-title":"Bull. Acad. Pol. Sc."}],"container-title":["Asymptotic Analysis"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/ASY-151322","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:40:40Z","timestamp":1777380040000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.medra.org\/servlet\/aliasResolver?alias=iospress&doi=10.3233\/ASY-151322"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,11,9]]},"references-count":23,"journal-issue":{"issue":"3-4"},"URL":"https:\/\/doi.org\/10.3233\/asy-151322","relation":{},"ISSN":["1875-8576","0921-7134"],"issn-type":[{"value":"1875-8576","type":"electronic"},{"value":"0921-7134","type":"print"}],"subject":[],"published":{"date-parts":[[2015,11,9]]}}}