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Analysis of a system of nonlocal conservation laws for multi-commodity flow on networks
1. | Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Department Mathematik, Chair of Applied Mathematics 2, Cauerstraße 11, 91058 Erlangen, Germany, Germany, Germany |
2. | School of Mathematical Sciences and Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai 200433, China |
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ESAIM Control Optim. Calc. Var., 17 (2011), 353-379.
doi: 10.1051/cocv/2010007. |
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Discrete Contin. Dyn. Syst. Ser. B, 14 (2010), 1337-1359.
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doi: 10.1007/978-3-642-20308-4. |
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Birkhäuser Boston, 1984.
doi: 10.1007/978-1-4684-9486-0. |
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SIAM J. Control Optim., 52 (2014), 2141-2163.
doi: 10.1137/120873832. |
[16] |
Networks and Heterogeneous Media, 10 (2015), 295-320.
doi: 10.3934/nhm.2015.10.295. |
[17] |
Journal of Optimization Theory and Applications, 126 (2005), 589-616.
doi: 10.1007/s10957-005-5499-z. |
[18] |
in Constrained optimization and optimal control for partial differential equations, vol. 160 of Internat. Ser. Numer. Math., Birkhäuser/Springer Basel AG, Basel, 2012, 123-146.
doi: 10.1007/978-3-0348-0133-1_7. |
[19] |
Operations Res., 26 (1978), 209-236.
doi: 10.1287/opre.26.2.209. |
[20] |
IEEE Trans. Automat. Contr., 55 (2010), 2511-2526.
doi: 10.1109/TAC.2010.2046925. |
[21] |
American Mathematical Society, Providence, RI, 2009.
doi: 10.1090/gsm/105. |
[22] |
Ann. Mat. Pura Appl. (4), 146 (1987), 65-96
doi: 10.1007/BF01762360. |
[23] |
Springer, 2011.
doi: 10.1007/978-1-4614-1135-2. |
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W. W.-Y. Wong, Compactness in $L^{2}$, 2013, Personal Communication.,, , (). Google Scholar |
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World Scientific Publishing Co. Inc., River Edge, NJ, 2000.
doi: 10.1142/9789812799531_0003. |
show all references
References:
[1] |
2nd edition, Elsevier/Academic Press, Amsterdam, 2003. |
[2] |
SIAM Journal on Numerical Analysis, 53 (2015), 963-983.
doi: 10.1137/140975255. |
[3] |
Oxford Mathematical Monographs, The Clarendon Press Oxford University Press, New York, 2000. Google Scholar |
[4] |
SIAM J. Appl. Math., 66 (2006), 896-920.
doi: 10.1137/040604625. |
[5] |
Operations Research, 54 (2006), 933-950.
doi: 10.1287/opre.1060.0321. |
[6] |
Networks, 8 (1978), 37-91.
doi: 10.1002/net.3230080107. |
[7] |
Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2006.
doi: 10.1137/1.9781611973488. |
[8] |
Numerische Mathematik, Springer Berlin Heidelberg, (2015), 1-25.
doi: 10.1007/s00211-015-0717-6. |
[9] |
Universitext, Springer, New York, 2011.
doi: 10.1007/978-0-387-70914-7. |
[10] |
ESAIM Control Optim. Calc. Var., 17 (2011), 353-379.
doi: 10.1051/cocv/2010007. |
[11] |
Discrete Contin. Dyn. Syst. Ser. B, 14 (2010), 1337-1359.
doi: 10.3934/dcdsb.2010.14.1337. |
[12] |
Princeton Landmarks in Mathematics, Princeton University Press, Princeton, NJ, 1962. |
[13] |
Intelligent Systems Reference Library, Springer, 2011.
doi: 10.1007/978-3-642-20308-4. |
[14] |
Birkhäuser Boston, 1984.
doi: 10.1007/978-1-4684-9486-0. |
[15] |
SIAM J. Control Optim., 52 (2014), 2141-2163.
doi: 10.1137/120873832. |
[16] |
Networks and Heterogeneous Media, 10 (2015), 295-320.
doi: 10.3934/nhm.2015.10.295. |
[17] |
Journal of Optimization Theory and Applications, 126 (2005), 589-616.
doi: 10.1007/s10957-005-5499-z. |
[18] |
in Constrained optimization and optimal control for partial differential equations, vol. 160 of Internat. Ser. Numer. Math., Birkhäuser/Springer Basel AG, Basel, 2012, 123-146.
doi: 10.1007/978-3-0348-0133-1_7. |
[19] |
Operations Res., 26 (1978), 209-236.
doi: 10.1287/opre.26.2.209. |
[20] |
IEEE Trans. Automat. Contr., 55 (2010), 2511-2526.
doi: 10.1109/TAC.2010.2046925. |
[21] |
American Mathematical Society, Providence, RI, 2009.
doi: 10.1090/gsm/105. |
[22] |
Ann. Mat. Pura Appl. (4), 146 (1987), 65-96
doi: 10.1007/BF01762360. |
[23] |
Springer, 2011.
doi: 10.1007/978-1-4614-1135-2. |
[24] |
W. W.-Y. Wong, Compactness in $L^{2}$, 2013, Personal Communication.,, , (). Google Scholar |
[25] |
World Scientific Publishing Co. Inc., River Edge, NJ, 2000.
doi: 10.1142/9789812799531_0003. |
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