History-dependent scalar conservation laws

Pierangelo Marcati; Bruno Rubino

Rendiconti del Seminario Matematico della Università di Padova (1996)

  • Volume: 96, page 195-204
  • ISSN: 0041-8994

How to cite


Marcati, Pierangelo, and Rubino, Bruno. "History-dependent scalar conservation laws." Rendiconti del Seminario Matematico della Università di Padova 96 (1996): 195-204. <http://eudml.org/doc/108409>.

author = {Marcati, Pierangelo, Rubino, Bruno},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {compensated compactness; global existence of weak solutions; linearly degenerate hyperbolic systems},
language = {eng},
pages = {195-204},
publisher = {Seminario Matematico of the University of Padua},
title = {History-dependent scalar conservation laws},
url = {http://eudml.org/doc/108409},
volume = {96},
year = {1996},

AU - Marcati, Pierangelo
AU - Rubino, Bruno
TI - History-dependent scalar conservation laws
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1996
PB - Seminario Matematico of the University of Padua
VL - 96
SP - 195
EP - 204
LA - eng
KW - compensated compactness; global existence of weak solutions; linearly degenerate hyperbolic systems
UR - http://eudml.org/doc/108409
ER -


  1. [1] J.M. Ball, A version of the fundamental theorem for Young measures, in D. SERRE, editor, Proc. Conf. on Partial Differential Equation and Continuum Models of Phase Transitions, Springer-Verlag (1988). Zbl0991.49500MR1036070
  2. [2] G.-Q. Chen - T.-P. LIU, Zero relaxation and dissipation Limits for hyperbolic conservation laws, Comm. Pure Appl. Math., 46 (1993), pp. 755-781. Zbl0797.35113MR1213992
  3. [3] G.-Q. Chen - Y. Lu, The study on application way of the compensated compactness theory, Clin. Sci. Bull., 34 (1989), pp. 15-19. Zbl0685.35067MR1000841
  4. [4] C.M. Dafermos, Development of singularities in the motion of materials with fading memory, Arch. Rational Mech. Anal., 91 (1986), pp. 193-205. Zbl0595.73026MR806001
  5. [5] C.M. Dafermos, Estimates for conservation laws with little viscosity, SIAM J. Math. Anal., 18 (1987), pp. 409-421. Zbl0655.35055MR876280
  6. [6] C.M. Dafermos, Solutions in L ∞for a conservation law with memory, Analyse Mathématique et Applications, (1988), pp. 117-128. Zbl0686.35075
  7. [7] C.M. Dafermos - J.A. Nohel, Energy methods for nonlinear hyperbolic Volterra integrodifferential equations, Comm. Partial Differential Equations, 4 (1979), pp. 219-278. Zbl0464.45009MR522712
  8. [8] C.M. Dafermos - J.A. Nohel, A nonlinear hyperbolic Volterra equation in viscoelasticity, Amer. J. Math., suppl. dedicated to P. Hartman, (1982), pp. 87-116. Zbl0588.35016MR648457
  9. [9] W.J. Hrusa - J.A. Nohel, The Cauchy problem in one-dimensional nonlinear viscoelasticity, J. Differential Equations, 59 (1985), pp. 388-412. Zbl0535.35057MR807854
  10. [10] P. Lin, Young measure and application of compensated compactness to one-dimensional nonlinear elacstodynamics, Trans. Amer. Math. Soc., 329 (1992), pp. 377-413. Zbl0761.35061MR1049615
  11. [11] T.-P. Liu, Nonlinear waves for viscoelasticity with fading memory, J. Differential Equations, 76 (1988), pp. 26-46. Zbl0662.35004MR964611
  12. [12] R.C. Maccamy, A model for one-dimensional nonlinear viscoelasticity, Quart. Appl. Math., 35 (1977), pp. 21-33. Zbl0355.73041MR478939
  13. [13] P. Marcati, Relaxation and singular convergence for quasitinear hyperbolic systems, in L. BOCCARDO, M. A. HERRERO and A. TESEI, editors, First Italian-Spain Meeting on Nonlinear Analisis, pp. 140-148, Rome (1989), Quaderno IAC-CNR. 
  14. [14] P. Marcati - A. Milani, The one-dimensional Darcy's law as the limit of a compressible Euler flow, J. Differential Equations, 13 (1990), pp. 129-147. Zbl0715.35065MR1042662
  15. [15] P. Marcati - A. Milani - P. Secchi, Singular convergence of weak solutions for a quasilinear nonhomogeneous hyperbolic system, Manuscripta Math., 60 (1988), pp. 49-69. Zbl0617.35078MR920759
  16. [16] J.A. Nohel - R.C. Rogers, Development of singularities in nonlinear viscoelasticity, in Amorphous Polymers and Non-Newtonian Fluids, vol. 6, pp. 139-152, Springer Lecture Notes in Mathematics (1987), IMA Vol. Math. Appl. MR902188
  17. [17] M. Renardy - W.J. Hrusa - J.A. Nohel, Mathematical Problems in Viscoelasticity, John Wiley and Longmann Press (1987). Zbl0719.73013MR919738
  18. [18] M.E. Schonbek, Convergence of solutions to nonlinear dispersive equations, Comm. Partial Differential Equations, 7 (1982), pp. 959-1000. Zbl0496.35058MR668586

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