Decay of positive waves in nonlinear systems of conservation laws

Alberto Bressan; Rinaldo M. Colombo

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1998)

  • Volume: 26, Issue: 1, page 133-160
  • ISSN: 0391-173X

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Bressan, Alberto, and Colombo, Rinaldo M.. "Decay of positive waves in nonlinear systems of conservation laws." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 26.1 (1998): 133-160. <http://eudml.org/doc/84318>.

@article{Bressan1998,
author = {Bressan, Alberto, Colombo, Rinaldo M.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {one space dimension; entropy solutions; wave-front tracking approximations; BV solutions},
language = {eng},
number = {1},
pages = {133-160},
publisher = {Scuola normale superiore},
title = {Decay of positive waves in nonlinear systems of conservation laws},
url = {http://eudml.org/doc/84318},
volume = {26},
year = {1998},
}

TY - JOUR
AU - Bressan, Alberto
AU - Colombo, Rinaldo M.
TI - Decay of positive waves in nonlinear systems of conservation laws
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1998
PB - Scuola normale superiore
VL - 26
IS - 1
SP - 133
EP - 160
LA - eng
KW - one space dimension; entropy solutions; wave-front tracking approximations; BV solutions
UR - http://eudml.org/doc/84318
ER -

References

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  1. [1] P. Baiti - A. Bressan, Lower Semicontinuity of Weighted Path Length in BV, In "Geometrical Optics and Related Topics", F. Colombini and N. Lerner (eds.), Birkäuser, 1997. Zbl0891.35089MR2033490
  2. [2] A. Bressan, Global solutions to systems of conservation laws by wave-front tracking, J. Math. Anal. Appl.170 (1992), 414-432. Zbl0779.35067MR1188562
  3. [3] A. Bressan, "Lecture Notes on Systems of Conservation Laws", S.I.S.S.A., Trieste, 1995. 
  4. [4] A. Bressan, The unique limit of the Glimm scheme, Arch. Rational Mech. Anal.130 (1995), 205-230. Zbl0835.35088MR1337114
  5. [5] A. Bressan, The semigroup approach to systems of conservation laws, Mathematica Contemporanea10 (1996), 21-74. Zbl0866.35064MR1425453
  6. [6] A. Bressan - R.M. Colombo, The semigroup generated by 2 x 2 conservation laws, Arch. Rational Mech. Anal.133 (1995), 1-75. Zbl0849.35068MR1367356
  7. [7] A. Bressan - R.M. Colombo, Unique solutions of 2 x 2 conservation laws with large data, Indiana Univ. Math. J.44 (1995), 677-725. Zbl0852.35092MR1375345
  8. [8] A. Bressan - G. Crasta - B. Piccoli, Well posedness of the Cauchy Problem for n x n systems of conservation laws, preprint S.I.S.S.A., Trieste, 1996. Zbl0958.35001
  9. [9] C.M. Dafermos, Generalized characteristics in hyperbolic systems of conservation laws, Arch. Rational Mech. Anal.107 (1989),127-155. Zbl0714.35046
  10. [10] A.F. Filippov, "Differential Equations with Discontinuous Righthand Sides", Kluwer Academic Publisher, Dordrecht, 1988. Zbl0664.34001
  11. [11] J. Glimm, Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math.18 (1965), 697-715. Zbl0141.28902
  12. [12] P. Lax, Hyperbolic systems of conservation laws II, Comm. Pure Appl. Math.10 (1957), 537-566. Zbl0081.08803
  13. [13] O. Oleinik, Discontinuous solutions of nonlinear differential equations, Usp. Mat. Nauk.12 (1957), 3-73; English translation: Amer. Math. Soc. Transl.26 (1963), 95-172. Zbl0131.31803
  14. [14] M. Schatzman, Continuous Glimm functionals and uniquess of solutions of the Riemann problem, Indiana Univ. Math. J.34 (1985), 533-589. Zbl0579.35053
  15. [15] J. Smoller, "Shock Waves and Reaction-Diffusion Equations", Springer-Verlag, New York, 1983. Zbl0508.35002
  16. [16] B. Temple, Systems of conservation laws with invariant submanifolds, Trans. Amer.Math. Soc.280 (1983), 781-795. Zbl0559.35046

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