{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T08:28:49Z","timestamp":1767860929600,"version":"3.49.0"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2021,8,10]],"date-time":"2021-08-10T00:00:00Z","timestamp":1628553600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,8,10]],"date-time":"2021-08-10T00:00:00Z","timestamp":1628553600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math. Control Signals Syst."],"published-print":{"date-parts":[[2022,3]]},"DOI":"10.1007\/s00498-021-00301-2","type":"journal-article","created":{"date-parts":[[2021,8,10]],"date-time":"2021-08-10T10:22:19Z","timestamp":1628590939000},"page":"37-65","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Exponential stability of a general slope limiter scheme for scalar conservation laws subject to a dissipative boundary condition"],"prefix":"10.1007","volume":"34","author":[{"given":"Mathias","family":"Dus","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,8,10]]},"reference":[{"issue":"1","key":"301_CR1","doi-asserted-by":"publisher","first-page":"352","DOI":"10.1016\/j.jfa.2017.03.010","volume":"273","author":"F Alabau-Boussouira","year":"2017","unstructured":"Alabau-Boussouira F, Privat Y, Tr\u00e9lat E (2017) Nonlinear damped partial differential equations and their uniform discretizations. J Funct Anal 273(1):352\u2013403","journal-title":"J Funct Anal"},{"issue":"1","key":"301_CR2","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1007\/s00205-010-0389-4","volume":"201","author":"B Andreianov","year":"2011","unstructured":"Andreianov B, Karlsen K-H, Risebro N-H (2011) A theory of $$L^1$$-dissipative solvers for scalar conservation laws with discontinuous flux. Arch Ration Mech Anal 201(1):27\u201386","journal-title":"Arch Ration Mech Anal"},{"issue":"11","key":"301_CR3","doi-asserted-by":"publisher","first-page":"5913","DOI":"10.3934\/dcds.2017257","volume":"37","author":"BP Andreianov","year":"2017","unstructured":"Andreianov BP, Coclite GM, Donadello C (2017) Well-posedness for vanishing viscosity solutions of scalar conservation laws on a network. Discrete Contin Dyn Syst 37(11):5913\u20135942","journal-title":"Discrete Contin Dyn Syst"},{"issue":"3","key":"301_CR4","doi-asserted-by":"publisher","first-page":"916","DOI":"10.1137\/S0036139997332099","volume":"60","author":"A Aw","year":"2000","unstructured":"Aw A, Rascle M (2000) Resurrection of \u201csecond order\" models of traffic flow. SIAM J Appl Math 60(3):916\u2013938","journal-title":"SIAM J Appl Math"},{"issue":"2","key":"301_CR5","doi-asserted-by":"publisher","first-page":"121","DOI":"10.3934\/mcrf.2013.3.121","volume":"3","author":"MK Banda","year":"2013","unstructured":"Banda MK, Herty M (2013) Numerical discretization of stabilization problems with boundary controls for systems of hyperbolic conservation laws. Math Control Relat Fields 3(2):121\u2013142","journal-title":"Math Control Relat Fields"},{"issue":"11","key":"301_CR6","doi-asserted-by":"publisher","first-page":"900","DOI":"10.1016\/j.sysconle.2011.07.008","volume":"60","author":"G Bastin","year":"2011","unstructured":"Bastin G, Coron J-M (2011) On boundary feedback stabilization of non-uniform linear $$2\\times 2$$ hyperbolic systems over a bounded interval. Syst Control Lett 60(11):900\u2013906","journal-title":"Syst Control Lett"},{"key":"301_CR7","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-32062-5","volume-title":"Stability and boundary stabilization of 1-D hyperbolic systems, volume\u00a088 of Progress in nonlinear differential equations and their applications","author":"G Bastin","year":"2016","unstructured":"Bastin G, Coron J-M (2016) Stability and boundary stabilization of 1-D hyperbolic systems, volume\u00a088 of Progress in nonlinear differential equations and their applications. Birkh\u00e4user\/Springer, Berlin"},{"issue":"10","key":"301_CR8","doi-asserted-by":"publisher","first-page":"2692","DOI":"10.1016\/j.automatica.2014.09.001","volume":"50","author":"P Bernard","year":"2014","unstructured":"Bernard P, Krstic M (2014) Adaptive output-feedback stabilization of non-local hyperbolic PDEs. Autom J IFAC 50(10):2692\u20132699","journal-title":"Autom J IFAC"},{"key":"301_CR9","doi-asserted-by":"crossref","unstructured":"Bressan A (2000) Hyperbolic systems of conservation laws, volume 20 of Oxford lecture series in mathematics and its applications. Oxford University Press, Oxford. The one-dimensional Cauchy problem","DOI":"10.1093\/oso\/9780198507000.001.0001"},{"issue":"5","key":"301_CR10","doi-asserted-by":"publisher","first-page":"467","DOI":"10.1002\/(SICI)1099-1476(20000325)23:5<467::AID-MMA124>3.0.CO;2-7","volume":"23","author":"C Chainais-Hillairet","year":"2000","unstructured":"Chainais-Hillairet C (2000) Second-order finite-volume schemes for a non-linear hyperbolic equation: error estimate. Math Methods Appl Sci 23(5):467\u2013490","journal-title":"Math Methods Appl Sci"},{"issue":"1","key":"301_CR11","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.jde.2016.09.016","volume":"262","author":"J-M Coron","year":"2017","unstructured":"Coron J-M, Ervedoza S, Ghoshal SS, Glass O, Perrollaz V (2017) Dissipative boundary conditions for $$2\\times 2$$ hyperbolic systems of conservation laws for entropy solutions in BV. J Differ Equ 262(1):1\u201330","journal-title":"J Differ Equ"},{"issue":"5","key":"301_CR12","doi-asserted-by":"publisher","first-page":"2646","DOI":"10.1137\/120902203","volume":"45","author":"J-M Coron","year":"2013","unstructured":"Coron J-M, Wang Z (2013) Output feedback stabilization for a scalar conservation law with a nonlocal velocity. SIAM J Math Anal 45(5):2646\u20132665","journal-title":"SIAM J Math Anal"},{"key":"301_CR13","doi-asserted-by":"crossref","unstructured":"Dus M (2020) Bv exponential stability for systems of scalar conservation laws using saturated feedback, preprint (to appear in SIAM SICON)","DOI":"10.1137\/20M1323837"},{"key":"301_CR14","doi-asserted-by":"crossref","unstructured":"Dus M (2021) Exponential stability of a general slope limiter scheme for scalar conservation laws subject to a dissipative boundary condition. Preprint, January","DOI":"10.1007\/s00498-021-00301-2"},{"issue":"2","key":"301_CR15","doi-asserted-by":"publisher","first-page":"298","DOI":"10.1051\/cocv:2008071","volume":"16","author":"S Ervedoza","year":"2010","unstructured":"Ervedoza S (2010) Observability properties of a semi-discrete 1D wave equation derived from a mixed finite element method on nonuniform meshes. ESAIM Control Optim Calc Var 16(2):298\u2013326","journal-title":"ESAIM Control Optim Calc Var"},{"issue":"1","key":"301_CR16","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1016\/j.matpur.2008.09.002","volume":"91","author":"S Ervedoza","year":"2009","unstructured":"Ervedoza S, Zuazua E (2009) Uniformly exponentially stable approximations for a class of damped systems. J Math Pures Appl (9) 91(1):20\u201348","journal-title":"J Math Pures Appl (9)"},{"key":"301_CR17","doi-asserted-by":"crossref","unstructured":"Eymard R, Gallou\u00ebt T, Herbin R (2000) Finite volume methods. In: Solution of equation in $$\\mathbb{R}^n$$ (Part 3), techniques of scientific computing (Part 3), volume\u00a07 of Handbook of numerical analysis. Elsevier, pp 713\u20131018","DOI":"10.1016\/S1570-8659(00)07005-8"},{"issue":"3","key":"301_CR18","doi-asserted-by":"publisher","first-page":"517","DOI":"10.3934\/mcrf.2019024","volume":"9","author":"S Gerster","year":"2019","unstructured":"Gerster S, Herty M (2019) Discretized feedback control for systems of linearized hyperbolic balance laws. Math Control Relat Fields 9(3):517\u2013539","journal-title":"Math Control Relat Fields"},{"issue":"3","key":"301_CR19","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1016\/0021-9991(83)90136-5","volume":"49","author":"A Harten","year":"1983","unstructured":"Harten A (1983) High resolution schemes for hyperbolic conservation laws. J Comput Phys 49(3):357\u2013393","journal-title":"J Comput Phys"},{"key":"301_CR20","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1051\/cocv\/2018059","volume":"25","author":"A Hayat","year":"2019","unstructured":"Hayat A (2019) On boundary stability of inhomogeneous $$2\\times 2$$ 1-D hyperbolic systems for the $$C^1$$ norm. ESAIM Control Optim Calc Var 25:31","journal-title":"ESAIM Control Optim Calc Var"},{"issue":"4","key":"301_CR21","doi-asserted-by":"publisher","first-page":"527","DOI":"10.1007\/s002110050156","volume":"71","author":"D Kr\u00f6ner","year":"1995","unstructured":"Kr\u00f6ner D, Noelle S, Rokyta M (1995) Convergence of higher order upwind finite volume schemes on unstructured grids for scalar conservation laws in several space dimensions. Numer Math 71(4):527\u2013560","journal-title":"Numer Math"},{"issue":"123","key":"301_CR22","first-page":"228","volume":"81","author":"SN Kru\u017ekov","year":"1970","unstructured":"Kru\u017ekov SN (1970) First order quasilinear equations with several independent variables. Mat Sb (NS) 81(123):228\u2013255","journal-title":"Mat Sb (NS)"},{"key":"301_CR23","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511791253","volume-title":"Finite volume methods for hyperbolic problems. Cambridge texts in applied mathematics","author":"RJ LeVeque","year":"2002","unstructured":"LeVeque RJ (2002) Finite volume methods for hyperbolic problems. Cambridge texts in applied mathematics. Cambridge University Press, Cambridge"},{"issue":"11\u201312","key":"301_CR24","doi-asserted-by":"publisher","first-page":"647","DOI":"10.1016\/j.crma.2010.03.020","volume":"348","author":"A Marica","year":"2010","unstructured":"Marica A, Zuazua E (2010) Localized solutions for the finite difference semi-discretization of the wave equation. C R Math Acad Sci Paris 348(11\u201312):647\u2013652","journal-title":"C R Math Acad Sci Paris"},{"issue":"181","key":"301_CR25","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1090\/S0025-5718-1988-0917817-X","volume":"50","author":"S Osher","year":"1988","unstructured":"Osher S, Tadmor E (1988) On the convergence of difference approximations to scalar conservation laws. Math Comp 50(181):19\u201351","journal-title":"Math Comp"},{"issue":"4","key":"301_CR26","doi-asserted-by":"publisher","first-page":"885","DOI":"10.1142\/S0219891605000658","volume":"2","author":"EYu Panov","year":"2005","unstructured":"Panov EYu (2005) Existence of strong traces for generalized solutions of multidimensional scalar conservation laws. J Hyperbolic Differ Equ 2(4):885\u2013908","journal-title":"J Hyperbolic Differ Equ"},{"issue":"5","key":"301_CR27","doi-asserted-by":"publisher","first-page":"995","DOI":"10.1137\/0721062","volume":"21","author":"PK Sweby","year":"1984","unstructured":"Sweby PK (1984) High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM J Numer Anal 21(5):995\u20131011","journal-title":"SIAM J Numer Anal"},{"issue":"3","key":"301_CR28","doi-asserted-by":"publisher","first-page":"563","DOI":"10.1007\/s00211-002-0442-9","volume":"95","author":"LR T\u00e9bou","year":"2003","unstructured":"T\u00e9bou LR, Zuazua E (2003) Uniform exponential long time decay for the space semi-discretization of a locally damped wave equation via an artificial numerical viscosity. Numer Math 95(3):563\u2013598","journal-title":"Numer Math"},{"issue":"1\u20133","key":"301_CR29","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1007\/s10444-004-7629-9","volume":"26","author":"LT Tebou","year":"2007","unstructured":"Tebou LT, Zuazua E (2007) Uniform boundary stabilization of the finite difference space discretization of the $$1-d$$ wave equation. Adv Comput Math 26(1\u20133):337\u2013365","journal-title":"Adv Comput Math"},{"key":"301_CR30","series-title":"London Mathematical Society lecture note series","first-page":"31","volume-title":"Stabilization of semilinear PDEs, and uniform decay under discretization","author":"E Tr\u00e9lat","year":"2017","unstructured":"Tr\u00e9lat E (2017) Stabilization of semilinear PDEs, and uniform decay under discretization. London Mathematical Society lecture note series. Cambridge University Press, Cambridge, pp 31\u201376"},{"key":"301_CR31","unstructured":"Van\u00a0Leer B (1979) Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov\u2019s method [J Comput Phys 32(1):101\u2013136]. volume 135, pages 227\u2013248. 1997. With an introduction by Ch. Hirsch, Commemoration of the 30th anniversary of J Comput Phys"},{"issue":"3","key":"301_CR32","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1007\/s002050100157","volume":"160","author":"A Vasseur","year":"2001","unstructured":"Vasseur A (2001) Strong traces for solutions of multidimensional scalar conservation laws. Arch Ration Mech Anal 160(3):181\u2013193","journal-title":"Arch Ration Mech Anal"},{"issue":"2","key":"301_CR33","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1137\/S0036144503432862","volume":"47","author":"E Zuazua","year":"2005","unstructured":"Zuazua E (2005) Propagation, observation, and control of waves approximated by finite difference methods. SIAM Rev 47(2):197\u2013243","journal-title":"SIAM Rev"}],"container-title":["Mathematics of Control, Signals, and Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00498-021-00301-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00498-021-00301-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00498-021-00301-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,7]],"date-time":"2023-11-07T05:10:31Z","timestamp":1699333831000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00498-021-00301-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,10]]},"references-count":33,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,3]]}},"alternative-id":["301"],"URL":"https:\/\/doi.org\/10.1007\/s00498-021-00301-2","relation":{},"ISSN":["0932-4194","1435-568X"],"issn-type":[{"value":"0932-4194","type":"print"},{"value":"1435-568X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,8,10]]},"assertion":[{"value":"10 February 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 July 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 August 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}