riemann.bib

@article{greenberg1997analysis,
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@article{isaacson1992nonlinear,
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@article{holden1995mathematical,
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  author = {Holden, Helge and Risebro, Nils Henrik},
  journal = {SIAM Journal on Mathematical Analysis},
  volume = {26},
  number = {4},
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  year = {1995},
  publisher = {SIAM}
}
@book{garavello2006traffic,
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  year = {2006},
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@article{delle2014pde,
  title = {A PDE-ODE model for a junction with ramp buffer},
  author = {Delle Monache, Maria Laura and Reilly, Jack and Samaranayake, Samitha and Krichene, Walid and Goatin, Paola and Bayen, Alexandre M},
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@article{edwards2008non,
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  year = {2008}
}
@article{leveque2004dynamics,
  title = {The dynamics of pressureless dust clouds and delta waves},
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  pages = {315--327},
  year = {2004},
  publisher = {World Scientific}
}
@article{craik1981circular,
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@article{watson1964radial,
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@article{zobeyer2013radial,
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  journal = {Journal of Engineering Mechanics},
  volume = {140},
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  year = {2013},
  publisher = {American Society of Civil Engineers}
}
@article{mochon1987analysis,
  author = {Mochon, S},
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  title = {An analysis of the traffic on highways with changing surface conditions},
  volume = {9},
  year = {1987}
}
@article{2012_ketchesonleveque_periodic,
  author = {Ketcheson, David I. and LeVeque, Randall J.},
  journal = {Communications in Mathematical Sciences},
  number = {3},
  pages = {859--874},
  title = {Shock Dynamics in Layered Periodic Media},
  volume = {10},
  year = {2012}
}
@article{leveque2003,
  author = {LeVeque, Randall J. and Yong, Darryl H.},
  journal = {SIAM Journal on Applied Mathematics},
  pages = {1539--1560},
  title = {{Solitary waves in layered nonlinear media}},
  volume = {63},
  year = {2003}
}
@article{leveque2002,
  author = {LeVeque, Randall J.},
  journal = {International Journal for Numerical Methods in Fluids},
  pages = {93--104},
  title = {{Finite-volume methods for non-linear elasticity in heterogeneous media}},
  volume = {40},
  year = {2002}
}
@article{lighthill1955kinematic,
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  author = {Lighthill, Michael J and Whitham, Gerald Beresford},
  journal = {Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences},
  volume = {229},
  number = {1178},
  pages = {317--345},
  year = {1955},
  organization = {The Royal Society}
}
@article{richards1956shock,
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  number = {1},
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  year = {1956},
  publisher = {INFORMS}
}
@book{toro2013riemann,
  title = {Riemann solvers and numerical methods for fluid dynamics: a practical introduction},
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}
@book{fvmhp,
  author = {R. J. LeVeque},
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  year = {2002}
}
@article{osher1984,
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  year = {1984},
  doi = {10.1137/0721016}
}
@article{delrazo2017,
  author = {M. J. Del Razo and R. J. LeVeque},
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  pages = {B486-B507},
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  volume = {39(3)},
  year = {2017},
  doi = {10.1137/16M1067834}
}
@article{del2016computational,
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  author = {Del Razo, Mauricio J and Morofuji, Yoichi and Meabon, James S and Huber, B Russell and Peskind, Elaine R and Banks, William A and Mourad, Pierre D and Leveque, Randall J and Cook, David G},
  journal = {SIAM Journal on Scientific Computing},
  volume = {38},
  number = {3},
  pages = {B347--B374},
  year = {2016}
}
@article{Ivings1998,
  title = {On {Riemann} solvers for compressible liquids},
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  journal = {International Journal for Numerical Methods in Fluids},
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  year = {1998}
}
@article{Burger2008,
  author = {B{\"u}rger, Raimund and Karlsen, Kenneth H.},
  journal = {Journal of Engineering Mathematics},
  month = jan,
  number = {3-4},
  pages = {241--247},
  title = {{Conservation laws with discontinuous flux: a short introduction}},
  volume = {60},
  year = {2008}
}
@article{HLL,
  title = {On upstream differencing and Godunov-type schemes for hyperbolic
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  author = {Harten, Amiram and Lax, Peter D and Leer, Bram van},
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  number = {1},
  pages = {35--61},
  year = {1983},
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}
@book{riemann1860fortpflanzung,
  title = {{\"U}ber die Fortpflanzung ebener Luftwellen von endlicher Schwingungsweite},
  author = {Riemann, Bernhard and others},
  year = {1860},
  publisher = {Verlag der Dieterichschen Buchhandlung}
}
@article{stokes1848liv,
  title = {On a difficulty in the theory of Sound},
  author = {Stokes, George Gabriel},
  journal = {The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science: Series 3},
  volume = {33},
  number = {223},
  pages = {349--356},
  year = {1848}
}
@misc{dafermos2010hyperbolic,
  title = {Hyperbolic conservation laws in continuum physics, volume 325 of Fundamental Principles of Mathematical Sciences},
  author = {Dafermos, Constantine M},
  year = {2010},
  publisher = {Springer-Verlag, Berlin,}
}
@book{liu2000hyperbolic,
  author = {Liu, T.},
  title = {Hyperbolic and Viscous Conservation Laws},
  publisher = {Society for Industrial and Applied Mathematics},
  year = {2000},
  doi = {10.1137/1.9780898719420}
}
@article{godunov1959difference,
  title = {A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics},
  author = {Godunov, Sergei Konstantinovich},
  journal = {Matematicheskii Sbornik},
  volume = {89},
  number = {3},
  pages = {271--306},
  year = {1959},
  publisher = {Russian Academy of Sciences, Steklov Mathematical Institute of Russian Academy of Sciences}
}
@article{Roe1981,
  title = {Approximate {Riemann} solvers, parameter vectors, and difference schemes},
  author = {Roe, Philip L},
  journal = {Journal of computational physics},
  volume = {43},
  number = {2},
  pages = {357--372},
  year = {1981}
}
@book{trangenstein2009,
  author = {J. A. Trangenstein},
  title = {Numerical Solution of Hyperbolic Partial Differential Equations},
  publisher = {Cambridge University Press},
  year = {2009}
}
@book{hesthaven2018,
  author = {J. S. Hesthaven},
  title = {Numerical Methods for Conservation Laws},
  publisher = {SIAM},
  year = {2018}
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@book{rjl:eth,
  author = {R. J. LeVeque},
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  year = {1990},
  publisher = {Birkh{\"a}user-Verlag}
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@book{kroener,
  author = {D. Kr{\"o}ner},
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  year = {1997},
  publisher = {Wiley-Teubner series}
}
@book{god-rav,
  author = {E. Godlewski and P.-A. Raviart},
  title = {Numerical Approximation of Hyperbolic Systems of Conservation Laws},
  year = {1996},
  publisher = {Springer-Verlag},
  address = {New York}
}
@book{lax:cbms,
  author = {P. D. Lax},
  title = {Hyperbolic Systems of Conservation Laws and the Mathematical Theory
  of Shock Waves},
  year = {1972},
  publisher = {SIAM Regional Conference Series in Applied Mathematics, \#11}
}
@article{godunov,
  author = {S. K. Godunov},
  journal = {Mat. Sb.},
  pages = {271--306},
  title = {A difference method for numerical calculation of discontinuous 
             solutions of the equations of hydrodynamics},
  volume = {47},
  year = {1959}
}

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