Hyperbolic systems, entropy and the method of finite volumes

Mirko Rokyta

Pokroky matematiky, fyziky a astronomie (2002)

  • Volume: 47, Issue: 4, page 287-297
  • ISSN: 0032-2423

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Rokyta, Mirko. "Hyperbolické systémy, entropie a metoda konečných objemů." Pokroky matematiky, fyziky a astronomie 47.4 (2002): 287-297. <http://eudml.org/doc/196393>.

@article{Rokyta2002,
author = {Rokyta, Mirko},
journal = {Pokroky matematiky, fyziky a astronomie},
keywords = {Cauchy problem; hyperbolic conservation law; finite volumes},
language = {cze},
number = {4},
pages = {287-297},
publisher = {Jednota českých matematiků a fyziků Union of Czech Mathematicians and Physicists},
title = {Hyperbolické systémy, entropie a metoda konečných objemů},
url = {http://eudml.org/doc/196393},
volume = {47},
year = {2002},
}

TY - JOUR
AU - Rokyta, Mirko
TI - Hyperbolické systémy, entropie a metoda konečných objemů
JO - Pokroky matematiky, fyziky a astronomie
PY - 2002
PB - Jednota českých matematiků a fyziků Union of Czech Mathematicians and Physicists
VL - 47
IS - 4
SP - 287
EP - 297
LA - cze
KW - Cauchy problem; hyperbolic conservation law; finite volumes
UR - http://eudml.org/doc/196393
ER -

References

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  1. Bressan, A., Hyperbolic systems of conservation laws. The one dimensional Cauchy problem, Oxford University Press 1998. (1998) Zbl0911.35070MR1816648
  2. Glimm, J., Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math. 18 (1965), 697–715. (1965) Zbl0141.28902MR0194770
  3. Godlewski, E., Raviart, P. A., Hyperbolic Systems of Conservation Laws, Mathematiques & Applications, S. M. A. I., Ellipses, Paris 1991 (in English). (1991) Zbl0768.35059MR1304494
  4. Kröner, D., Numerical Schemes for Conservation Laws, Teubner, Leipzig–Stuttgart 1996. (1996) Zbl0872.76001
  5. Kröner, D., Rokyta, M., Convergence of upwind finite volume schemes for scalar conservation laws in two dimensions, SIAM J. Numer. Anal. 31, no. 2 (1994), 324–343. (1994) Zbl0856.65104MR1276703
  6. Kružkov, S. N., First order quasilinear equations in several independent variables, Math. USSR Sbornik 10, no. 2 (1970), 217–243 (in English). (1970) Zbl0191.39703
  7. Lax, P. D., Hyperbolic systems of conservation laws II, Comm. Pure Appl. Math. 10 (1957), 537–566. (1957) Zbl0081.08803MR0093653
  8. Málek, J., Nečas, J., Rokyta, M., Růžička, M., Weak and measure-valued solutions to evolutionary partial differential equations, Chapman & Hall 1996. (1996) Zbl0851.35002
  9. Rauch, J., BV estimates fail for most quasilinear hyperbolic systems in dimension greater than one, Comm. Math. Phys. 106 (1986), 481–484. (1986) Zbl0619.35073MR0859822
  10. Rokyta, M., A suitable replacement of the BV condition for finite volume schemes on unstructured grids, In: Numerical Modelling in Continuum Mechanics, Feistauer, M., Rannacher, R., Kozel, K. (eds.), 267–274, Matfyzpress, Praha 2001. (2001) 
  11. Serre, D., Systemes de lois de conservation, Diderot Editeur, 1996. (1996) Zbl0930.35003
  12. Sever, M., Uniqueness failure for entropy solutions of hyperbolic systems of conservation laws, Comm. Pure Appl. Math. 42 (1989), 173–183. (1989) Zbl0645.35063MR0978703
  13. Smoller, J., Shock Waves and Reaction-Diffusion Equations, Grundlehren der math. Wissenschaften, Bd. 258, Springer-Verlag, Berlin–Heidelberg–New York, 1983 (1st ed.), 1994 (2nd ed.). (1983) Zbl0508.35002MR1301779

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