Construction of entropy solutions for one dimensional elastodynamics via time discretisation
Sophia Demoulini; David M. A. Stuart; Athanasios E. Tzavaras
Annales de l'I.H.P. Analyse non linéaire (2000)
- Volume: 17, Issue: 6, page 711-731
- ISSN: 0294-1449
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topDemoulini, Sophia, Stuart, David M. A., and Tzavaras, Athanasios E.. "Construction of entropy solutions for one dimensional elastodynamics via time discretisation." Annales de l'I.H.P. Analyse non linéaire 17.6 (2000): 711-731. <http://eudml.org/doc/78506>.
@article{Demoulini2000,
author = {Demoulini, Sophia, Stuart, David M. A., Tzavaras, Athanasios E.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {weak convergence; variational approximation scheme; one-dimensional elastodynamics; time discretisation; weak solution; entropy inequalities; positive spatial derivative; longitudinal motions},
language = {eng},
number = {6},
pages = {711-731},
publisher = {Gauthier-Villars},
title = {Construction of entropy solutions for one dimensional elastodynamics via time discretisation},
url = {http://eudml.org/doc/78506},
volume = {17},
year = {2000},
}
TY - JOUR
AU - Demoulini, Sophia
AU - Stuart, David M. A.
AU - Tzavaras, Athanasios E.
TI - Construction of entropy solutions for one dimensional elastodynamics via time discretisation
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2000
PB - Gauthier-Villars
VL - 17
IS - 6
SP - 711
EP - 731
LA - eng
KW - weak convergence; variational approximation scheme; one-dimensional elastodynamics; time discretisation; weak solution; entropy inequalities; positive spatial derivative; longitudinal motions
UR - http://eudml.org/doc/78506
ER -
References
top- [1] Ball J., Remarques sur l'existence et la régularité des solutions d'élastostatique non linéaire, in: Berestykci H., Brezis H. (Eds.), Recent Contributions of Nonlinear PDE, Pitman Research Notes in Mathematics50, Pitman, Boston, 1981, pp. 50- 62. Zbl0466.73012MR639745
- [2] Chen G.-Q., Frid H., Decay of entropy solutions of nonlinear conservation laws, Arch. Rational Mech. Anal.146 (1999) 95-127. Zbl0942.35031MR1718482
- [3] Dafermos C., Estimates for conservation laws with little viscosity, SIAM J. Math. Anal.18 (1987) 409-421. Zbl0655.35055MR876280
- [4] Demoulini S., Young measure solutions for nonlinear evolutionary systems of mixed type, Annales de l'I.H.P., Analyse Non Linéaire14 (1) (1997) 143-162. Zbl0871.35065MR1437192
- [5] Demoulini S., Weak solutions for a class of nonlinear systems of viscoelasticity, Arch. Rat. Mech. Analysis, to appear. Zbl0991.74021MR1808121
- [6] Demoulini S., Stuart D., Tzavaras A., A variational approximation scheme for three dimensional elastodynamics with polyconvex energy, preprint. Zbl0985.74024
- [7] DiPerna R., Convergence of approximate solutions to conservation laws, Arch. Rational Mech. Analysis82 (1983) 27-70. Zbl0519.35054MR684413
- [8] Godlewski E., Raviart P.-A., Numerical Approximation of Hyperbolic Systems of Conservation Laws, Springer-Verlag, New York, 1996. Zbl0860.65075MR1410987
- [9] Hörmander L., Lectures on Nonlinear Hyperbolic Differential Equations, Springer-Verlag, Berlin, 1997. Zbl0881.35001MR1466700
- [10] Kinderlehrer D., Perdregal P., Weak convergence of integrands and the Young measure representation, SIAM J. Math. Anal.23 (1992) 1-19. Zbl0757.49014MR1145159
- [11] Lax P, Shock waves and entropy, in: Zarantonello E.H. (Ed.), Contributions to Nonlinear Functional Analysis, New York, Academic Press, 1971, pp. 603-634. Zbl0268.35014MR393870
- [12] Lin P, Young measures and an application of compensated compactness to one-dimensional nonlinear elastodynamics, Trans. Amer. Math. Soc.329 (1992) 377- 413. Zbl0761.35061MR1049615
- [13] Murat F, L'injection du cône positif de H-1 dans W-1,q est compacte pour tout q < 2, J. Math. Pures Appl.60 (1981) 309-322. Zbl0471.46020
- [14] Rieger M., Young-measure solutions for diffusion elasticity equations, preprint.
- [ 15] Serre D., Relaxation semi-linéaire et cinétique des systèmes de lois de conservation, preprint.
- [16] Serre D., Shearer J., Convergence with physical viscosity for nonlinear elasticity, 1993, (unpublished manuscript).
- [17] Shearer J., Global existence and compactness in Lp for the quasi-linear wave equation, Comm. Partial Diff. Eq.19 (1994) 1829-1877. Zbl0855.35078MR1301175
- [18] Tartar L., Compensated compactness and applications to partial differential quations, in: Knops Nonlinear Analysis and Mechanics, IV Heriot-Watt Symposium, Vol. IV, Pitman Research Notes in Mathematics, Pitman, Boston, 1979, pp. 136- 192. Zbl0437.35004MR584398
- [19] Tzavaras A., Materials with internal variables and relaxation to conservation laws, Arch. Rational Mech. Anal.146 (1999) 129-155. Zbl0973.74005MR1718478
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