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ENTROPY-BASED MOMENT CLOSURE FOR KINETIC EQUATIONS: RIEMANN PROBLEM AND INVARIANT REGIONS

Team SIMPAF — INRIA Futurs & Université Lille 1, Laboratoire Paul Painlevé (UMR CNRS 8524), Cité scientifique, 59655 VILLENEUVE D'ASCQ Cedex, France

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THIERRY GOUDON

Team SIMPAF — INRIA Futurs & Université Lille 1, Laboratoire Paul Painlevé (UMR CNRS 8524), Cité scientifique, 59655 VILLENEUVE D'ASCQ Cedex, France

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https://doi.org/10.1142/S0219891606000951Cited by:8 (Source: Crossref)

Abstract

We study a nonlinear hyperbolic system of balance laws that arises from an entropy-based moment closure of a kinetic equation. We show that the corresponding homogeneous Riemann problem can be solved without smallness assumption, and we exhibit invariant regions.

Keywords:

AMSC: 35L60, 35Q99

References

C. Bardos, Lecture Notes in Mathematics 1047 (Springer, 1984) pp. 1–74. Google Scholar
C. Bardos, R. Santos and R. Sentis, Trans. Amer. Math. Soc. 284(2), 617 (1984), DOI: 10.2307/1999099. Crossref, Web of Science, Google Scholar
A. Bressan , Hyperbolic Systems of Conservation Laws ( Oxford University Press , 2000 ) . Crossref, Google Scholar
G.-Q. Chen and P. G. LeFloch, Arch. Ration. Mech. Anal. 153(3), 221 (2000), DOI: 10.1007/s002050000091. Crossref, Web of Science, Google Scholar
G.-Q. Chen and P. G. LeFloch, Arch. Ration. Mech. Anal. 166(1), 81 (2003), DOI: 10.1007/s00205-002-0229-2. Crossref, Web of Science, Google Scholar
K. N. Chueh, C. C. Conley and J. A. Smoller, Indiana Univ. Math. J. 26(2), 373 (1977), DOI: 10.1512/iumj.1977.26.26029. Crossref, Web of Science, Google Scholar
J.-F. Coulombel, F. Golse and T. Goudon, Asymp. Anal. 45(1–2), 1 (2005). Web of Science, Google Scholar
X. Ding, G.-Q. Chen and P. Luo, Commun. Math. Phys. 121(1), 63 (1989), DOI: 10.1007/BF01218624. Web of Science, Google Scholar
R. J. DiPerna, Commun. Math. Phys. 91(1), 1 (1983), DOI: 10.1007/BF01206047. Crossref, Web of Science, Google Scholar
D. Hoff, Trans. Amer. Math. Soc. 289(2), 591 (1985), DOI: 10.2307/2000254. Crossref, Web of Science, Google Scholar
H. Huang and Z. Wang, SIAM J. Math. Anal. 34(3), 595 (2002), DOI: 10.1137/S0036141002405819. Crossref, Web of Science, Google Scholar
P. D. Lax, Commun. Pure Appl. Math. 10, 537 (1957), DOI: 10.1002/cpa.3160100406. Crossref, Web of Science, Google Scholar
P. G. LeFloch and V. Shelukhin, Arch. Ration. Mech. Anal. 175(3), 389 (2005), DOI: 10.1007/s00205-004-0344-3. Crossref, Web of Science, Google Scholar
C. D. Levermore, J. Stat. Phys. 83(5–6), 1021 (1996), DOI: 10.1007/BF02179552. Crossref, Web of Science, Google Scholar
P.-L. Lions, B. Perthame and P. E. Souganidis, Commun. Pure Appl. Math. 49(6), 599 (1996), DOI: 10.1002/(SICI)1097-0312(199606)49:6<599::AID-CPA2>3.0.CO;2-5. Crossref, Web of Science, Google Scholar
P.-L. Lions, B. Perthame and E. Tadmor, Commun. Math. Phys. 163(2), 415 (1994), DOI: 10.1007/BF02102014. Crossref, Web of Science, Google Scholar
P. Marcati and A. Milani, J. Differential Equations 84(1), 129 (1990), DOI: 10.1016/0022-0396(90)90130-H. Crossref, Web of Science, Google Scholar
D. Serre , Systems of Conservation Laws. 1 ( Cambridge University Press , 1999 ) . Crossref, Google Scholar