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The many facets of internet topology and traffic
On the variational theory of traffic flow: well-posedness, duality and applications
1. | Department of Civil and Environmental Engineering, 416 McLaughlin Hall, Berkeley, CA 94707, United States |
[1] |
Gonzalo Dávila. Comparison principles for nonlocal Hamilton-Jacobi equations. Discrete and Continuous Dynamical Systems, 2022 doi: 10.3934/dcds.2022061 |
[2] |
Olga Bernardi, Franco Cardin. On $C^0$-variational solutions for Hamilton-Jacobi equations. Discrete and Continuous Dynamical Systems, 2011, 31 (2) : 385-406. doi: 10.3934/dcds.2011.31.385 |
[3] |
David McCaffrey. A representational formula for variational solutions to Hamilton-Jacobi equations. Communications on Pure and Applied Analysis, 2012, 11 (3) : 1205-1215. doi: 10.3934/cpaa.2012.11.1205 |
[4] |
Yasuhiro Fujita, Katsushi Ohmori. Inequalities and the Aubry-Mather theory of Hamilton-Jacobi equations. Communications on Pure and Applied Analysis, 2009, 8 (2) : 683-688. doi: 10.3934/cpaa.2009.8.683 |
[5] |
Xifeng Su, Lin Wang, Jun Yan. Weak KAM theory for HAMILTON-JACOBI equations depending on unknown functions. Discrete and Continuous Dynamical Systems, 2016, 36 (11) : 6487-6522. doi: 10.3934/dcds.2016080 |
[6] |
Manuel de León, David Martín de Diego, Miguel Vaquero. A Hamilton-Jacobi theory on Poisson manifolds. Journal of Geometric Mechanics, 2014, 6 (1) : 121-140. doi: 10.3934/jgm.2014.6.121 |
[7] |
Guillaume Costeseque, Jean-Patrick Lebacque. Discussion about traffic junction modelling: Conservation laws VS Hamilton-Jacobi equations. Discrete and Continuous Dynamical Systems - S, 2014, 7 (3) : 411-433. doi: 10.3934/dcdss.2014.7.411 |
[8] |
Claudio Marchi. On the convergence of singular perturbations of Hamilton-Jacobi equations. Communications on Pure and Applied Analysis, 2010, 9 (5) : 1363-1377. doi: 10.3934/cpaa.2010.9.1363 |
[9] |
Isabeau Birindelli, J. Wigniolle. Homogenization of Hamilton-Jacobi equations in the Heisenberg group. Communications on Pure and Applied Analysis, 2003, 2 (4) : 461-479. doi: 10.3934/cpaa.2003.2.461 |
[10] |
Giuseppe Marmo, Giuseppe Morandi, Narasimhaiengar Mukunda. The Hamilton-Jacobi theory and the analogy between classical and quantum mechanics. Journal of Geometric Mechanics, 2009, 1 (3) : 317-355. doi: 10.3934/jgm.2009.1.317 |
[11] |
Melvin Leok, Diana Sosa. Dirac structures and Hamilton-Jacobi theory for Lagrangian mechanics on Lie algebroids. Journal of Geometric Mechanics, 2012, 4 (4) : 421-442. doi: 10.3934/jgm.2012.4.421 |
[12] |
Sergey Rashkovskiy. Hamilton-Jacobi theory for Hamiltonian and non-Hamiltonian systems. Journal of Geometric Mechanics, 2020, 12 (4) : 563-583. doi: 10.3934/jgm.2020024 |
[13] |
Laura Caravenna, Annalisa Cesaroni, Hung Vinh Tran. Preface: Recent developments related to conservation laws and Hamilton-Jacobi equations. Discrete and Continuous Dynamical Systems - S, 2018, 11 (5) : i-iii. doi: 10.3934/dcdss.201805i |
[14] |
Fabio Camilli, Paola Loreti, Naoki Yamada. Systems of convex Hamilton-Jacobi equations with implicit obstacles and the obstacle problem. Communications on Pure and Applied Analysis, 2009, 8 (4) : 1291-1302. doi: 10.3934/cpaa.2009.8.1291 |
[15] |
Emeric Bouin. A Hamilton-Jacobi approach for front propagation in kinetic equations. Kinetic and Related Models, 2015, 8 (2) : 255-280. doi: 10.3934/krm.2015.8.255 |
[16] |
Gawtum Namah, Mohammed Sbihi. A notion of extremal solutions for time periodic Hamilton-Jacobi equations. Discrete and Continuous Dynamical Systems - B, 2010, 13 (3) : 647-664. doi: 10.3934/dcdsb.2010.13.647 |
[17] |
Antonio Avantaggiati, Paola Loreti, Cristina Pocci. Mixed norms, functional Inequalities, and Hamilton-Jacobi equations. Discrete and Continuous Dynamical Systems - B, 2014, 19 (7) : 1855-1867. doi: 10.3934/dcdsb.2014.19.1855 |
[18] |
Martino Bardi, Yoshikazu Giga. Right accessibility of semicontinuous initial data for Hamilton-Jacobi equations. Communications on Pure and Applied Analysis, 2003, 2 (4) : 447-459. doi: 10.3934/cpaa.2003.2.447 |
[19] |
Gui-Qiang Chen, Bo Su. Discontinuous solutions for Hamilton-Jacobi equations: Uniqueness and regularity. Discrete and Continuous Dynamical Systems, 2003, 9 (1) : 167-192. doi: 10.3934/dcds.2003.9.167 |
[20] |
Mihai Bostan, Gawtum Namah. Time periodic viscosity solutions of Hamilton-Jacobi equations. Communications on Pure and Applied Analysis, 2007, 6 (2) : 389-410. doi: 10.3934/cpaa.2007.6.389 |
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