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On interface transmission conditions for conservation laws with discontinuous flux of general shape. (English) Zbl 1336.35230
The authors investigate a scalar conservation law \(\partial_t u+\partial_x f(u;x)=0\) with jump-discontinuous at \(x=0\) flux function. They introduce the notion of a transmission map for the interface condition leading to the well-posedness of the Cauchy problem. Transmissions maps are also used to design convergent monotone numerical schemes based on one-sided approximate Riemann solvers. The paper is concluded by several examples coming from real-life applications.

MSC:
35L65 Hyperbolic conservation laws
35R05 PDEs with low regular coefficients and/or low regular data
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
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References:
[1] DOI: 10.1002/cpa.20346 · Zbl 1223.35222
[2] DOI: 10.1137/S003614290139562X · Zbl 1081.65082
[3] DOI: 10.1142/S0219891605000622 · Zbl 1093.35045
[4] Adimurthi, J. Math. Kyoto Univ. 43 pp 27– (2003) · Zbl 1063.35114
[5] DOI: 10.4310/CMS.2009.v7.n4.a8 · Zbl 1190.35148
[6] DOI: 10.1002/zamm.201200218 · Zbl 1297.76152
[7] DOI: 10.1016/j.aml.2012.02.044
[8] DOI: 10.1007/s10596-012-9329-8 · Zbl 1392.76033
[9] DOI: 10.1007/s10596-014-9403-5 · Zbl 1393.76114
[10] DOI: 10.1142/S0218202514500341 · Zbl 1307.35166
[11] DOI: 10.1007/s00211-009-0286-7 · Zbl 1196.65151
[12] DOI: 10.3934/nhm.2010.5.617 · Zbl 1270.35305
[13] DOI: 10.1007/s00205-010-0389-4 · Zbl 1261.35088
[14] DOI: 10.1137/130907963 · Zbl 1302.35263
[15] DOI: 10.1007/978-3-540-75712-2_98
[16] DOI: 10.1090/S0002-9947-2015-05988-1 · Zbl 1316.35184
[17] DOI: 10.3934/dcds.2012.32.1939 · Zbl 1246.35125
[18] DOI: 10.1017/S0308210500003863 · Zbl 1071.35079
[19] DOI: 10.1080/03605300500358095 · Zbl 1102.35064
[20] DOI: 10.1080/03605307908820117 · Zbl 0418.35024
[21] DOI: 10.1090/S0002-9947-98-02204-1 · Zbl 0955.65069
[22] DOI: 10.1137/0728036 · Zbl 0735.76071
[23] DOI: 10.1007/s10596-013-9345-3 · Zbl 1392.76035
[24] DOI: 10.1016/j.jmaa.2006.02.072 · Zbl 1160.35048
[25] DOI: 10.1007/s10665-007-9148-4 · Zbl 1200.76126
[26] DOI: 10.3934/nhm.2008.3.1 · Zbl 1173.35586
[27] DOI: 10.1137/07069314X · Zbl 1201.35022
[28] DOI: 10.1524/anly.2009.1036 · Zbl 1184.35111
[29] DOI: 10.1051/m2an/2009032 · Zbl 1171.76035
[30] DOI: 10.1137/090747981 · Zbl 1219.35136
[31] DOI: 10.1137/090747993 · Zbl 1219.35139
[32] DOI: 10.3934/nhm.2010.5.635 · Zbl 1262.35163
[33] DOI: 10.1007/s00028-010-0080-0 · Zbl 1232.35029
[34] DOI: 10.4171/IFB/210 · Zbl 1178.35196
[35] DOI: 10.1137/11082943X · Zbl 1262.35198
[36] Cancès C., SIAM J. Numer. Anal. 50 pp 336– (2012)
[37] DOI: 10.3934/nhm.2013.8.433 · Zbl 1275.35144
[38] DOI: 10.1007/BF00211103
[39] Chavent G., Studies in Mathematics and its Applications 17, in: Mathematical Models and Finite Elements for Reservoir Simulation (1986)
[40] DOI: 10.1016/j.jde.2006.10.014
[41] DOI: 10.1016/j.nonrwa.2008.08.002 · Zbl 1169.35360
[42] DOI: 10.1090/S0025-5718-1980-0551288-3
[43] DOI: 10.1090/S0002-9939-1980-0553381-X
[44] Dal Maso G., J. Math. Pures Appl. 74 pp 483– (1995)
[45] DOI: 10.1142/S0219891609001794 · Zbl 1180.35305
[46] DOI: 10.1016/0022-0396(88)90040-X · Zbl 0649.35057
[47] DOI: 10.1016/S1570-8659(00)07005-8
[48] DOI: 10.3934/nhm.2007.2.159 · Zbl 1142.35511
[49] DOI: 10.1137/0523032 · Zbl 0776.35034
[50] Godlewski E., Mathématiques & Applications 4, in: Hyperbolic Systems of Conservation Laws (1991) · Zbl 0768.35059
[51] DOI: 10.1057/jors.1958.9
[52] DOI: 10.1103/PhysRevE.75.046109
[53] DOI: 10.1016/0191-2615(95)00018-9
[54] DOI: 10.1023/A:1011574824970 · Zbl 0952.76085
[55] Karlsen K. H., Skr. K. Nor. Vidensk. Selsk. 3 pp 1– (2003)
[56] Kruzhkov S. N., Mat. Sb. (N.S.) 81 pp 228– (1970)
[57] DOI: 10.1016/j.jde.2008.03.011 · Zbl 1151.76033
[58] DOI: 10.1017/CBO9780511791253 · Zbl 1010.65040
[59] DOI: 10.1098/rspa.1955.0089 · Zbl 0064.20906
[60] DOI: 10.3934/dcds.2011.30.1191 · Zbl 1228.35144
[61] Otto F., C. R. Acad. Sci. Paris Sér. I Math. 322 pp 729– (1996)
[62] DOI: 10.1142/S0219891607001343 · Zbl 1144.35037
[63] DOI: 10.1287/opre.4.1.42
[64] DOI: 10.2118/14045-PA
[65] DOI: 10.1142/S0218202503002477 · Zbl 1078.35011
[66] DOI: 10.1137/S0036142999363668 · Zbl 0972.65060
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