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Communications in Partial Differential Equations Volume 20, 1995 - Issue 9-10
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Original Articles

A variational calculus for discontinuous solutions of systems of conservation laws

A variational calculus for discontinuous solutions

Bressan Alberto
&
Marson Andrea
Pages 1491-1552 | Published online: 08 May 2007

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Sebastian Pfaff & Stefan Ulbrich. (2017) Optimal control of scalar conservation laws by on/off-switching. Optimization Methods and Software 32:4, pages 904-939.
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Thibault Liard & Enrique Zuazua. (2023) Analysis and Numerical Solvability of Backward-Forward Conservation Laws. SIAM Journal on Mathematical Analysis 55:3, pages 1949-1968.
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Martin Gugat & Michael Herty. 2022. Numerical Control: Part A. Numerical Control: Part A 59 86 .
Alberto Bressan & Yucong Huang. (2019) Globally optimal departure rates for several groups of drivers. Mathematics in Engineering 1:3, pages 583-613.
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Gabriella Bretti, Emiliano Cristiani, Corrado Lattanzio, Amelio Maurizi & Benedetto Piccoli. (2018) Two algorithms for a fully coupled and consistently macroscopic PDE-ODEsystem modeling a moving bottleneck on a road. Mathematics in Engineering 1:1, pages 55-83.
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Michael Herty, Alexander Kurganov & Dmitry Kurochkin. 2018. Theory, Numerics and Applications of Hyperbolic Problems I. Theory, Numerics and Applications of Hyperbolic Problems I 691 706 .
Laurent Gosse & Enrique Zuazua. 2017. Innovative Algorithms and Analysis. Innovative Algorithms and Analysis 197 227 .
Elimboto M. Yohana & Mapundi K. Banda. (2016) High-order relaxation approaches for adjoint-based optimal control problems governed by nonlinear hyperbolic systems of conservation laws. Journal of Numerical Mathematics 24:1.
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Daniel J. Calderone, Lillian J. Ratliff & S. Shankar Sastry. (2015) Lane pricing via decision-theoretic lane changing model of driver behavior. Lane pricing via decision-theoretic lane changing model of driver behavior.
Sebastian Pfaff & Stefan Ulbrich. (2015) Optimal Boundary Control of Nonlinear Hyperbolic Conservation Laws with Switched Boundary Data. SIAM Journal on Control and Optimization 53:3, pages 1250-1277.
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Giacomo Albi, Michael Herty, Christian Jörres & Lorenzo Pareschi. (2014) Asymptotic preserving time‐discretization of optimal control problems for the Goldstein–Taylor model. Numerical Methods for Partial Differential Equations 30:6, pages 1770-1784.
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Helge Holden, Fabio Simone Priuli & Nils Henrik Risebro. (2014) On an inverse problem for scalar conservation laws. Inverse Problems 30:3, pages 035015.
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Yaobin Ou & Peicheng Zhu. (2013) The vanishing viscosity method for the sensitivity analysis of an optimal control problem of conservation laws in the presence of shocks. Nonlinear Analysis: Real World Applications 14:5, pages 1947-1974.
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C. D'Apice, R. Manzo & B. Piccoli. (2013) Numerical Schemes for the Optimal Input Flow of a Supply Chain. SIAM Journal on Numerical Analysis 51:5, pages 2634-2650.
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Sonja Steffensen, Michael Herty & Lorenzo Pareschi. 2013. System Modeling and Optimization. System Modeling and Optimization 136 144 .
Mapundi K. Banda & Michael Herty. (2010) Adjoint IMEX-based schemes for control problems governed by hyperbolic conservation laws. Computational Optimization and Applications 51:2, pages 909-930.
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Nathan Moshman, Sivaguru Sritharan & Garth Hobson. (2011) Optimal Control of Shock Wave Attenuation using Liquid Water Droplets with Application to Ignition Overpressure in Launch Vehicles. International Journal of Flow Control 3:4, pages 233-254.
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Carlos Castro & Enrique Zuazua. (2011) Flux identification for 1-𝐝 scalar conservation laws in the presence of shocks. Mathematics of Computation 80:276, pages 2025-2070.
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C. Castro, F. Palacios & E. Zuazua. 2010. Integral Methods in Science and Engineering, Volume 2. Integral Methods in Science and Engineering, Volume 2 65 90 .
Mauro Garavello & Benedetto Piccoli. 2007. Traffic and Granular Flow’05. Traffic and Granular Flow’05 383 392 .
Xiao-Biao Lin. (2006) Slow Eigenvalues of Self-similar Solutions of the Dafermos Regularization of a System of Conservation Laws: an Analytic Approach. Journal of Dynamics and Differential Equations 18:1, pages 1-52.
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G. M. Coclite, M. Garavello & B. Piccoli. (2005) Traffic Flow on a Road Network. SIAM Journal on Mathematical Analysis 36:6, pages 1862-1886.
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Marta Lewicka. (2005) Stability Conditions for Strong Rarefaction Waves. SIAM Journal on Mathematical Analysis 36:4, pages 1346-1369.
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Marta Lewicka. (2005) Lyapunov Functional for Solutions of Systems of Conservation Laws Containing a Strong Rarefaction. SIAM Journal on Mathematical Analysis 36:5, pages 1371-1399.
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Constantine M. Dafermos. 2005. Hyberbolic Conservation Laws in Continuum Physics. Hyberbolic Conservation Laws in Continuum Physics 511 536 .
Marta Lewicka. (2004) Well-Posedness for Hyperbolic Systems of Conservation Laws with Large BV Data. Archive for Rational Mechanics and Analysis 173:3, pages 415-445.
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Rinaldo M. Colombo & Alessandro Groli. (2004) On the optimization of the initial boundary value problem for a conservation law. Journal of Mathematical Analysis and Applications 291:1, pages 82-99.
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Xiao-Biao Lin & Stephen Schecter. (2003) Stability of Self-Similar Solutions of the Dafermos Regularization of a System of Conservation Laws. SIAM Journal on Mathematical Analysis 35:4, pages 884-921.
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Stefan Ulbrich. (2002) A Sensitivity and Adjoint Calculus for Discontinuous Solutions of Hyperbolic Conservation Laws with Source Terms. SIAM Journal on Control and Optimization 41:3, pages 740-797.
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Marta Lewicka. (2001) Stability Conditions for Patterns of Noninteracting Large Shock Waves. SIAM Journal on Mathematical Analysis 32:5, pages 1094-1116.
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Marta Lewicka. 2001. Hyperbolic Problems: Theory, Numerics, Applications. Hyperbolic Problems: Theory, Numerics, Applications 653 661 .
Paolo Baiti & Alberto Bressan. 1997. Geometrical Optics and Related Topics. Geometrical Optics and Related Topics 31 58 .

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