Construction of entropy solutions for one dimensional elastodynamics via time discretisation
Annales de l'I.H.P. Analyse non linéaire, Tome 17 (2000) no. 6, pp. 711-731. 
@article{AIHPC_2000__17_6_711_0,
     author = {Demoulini, Sophia and Stuart, David M. A. and Tzavaras, Athanasios E.},
     title = {Construction of entropy solutions for one dimensional elastodynamics via time discretisation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {711--731},
     publisher = {Gauthier-Villars},
     volume = {17},
     number = {6},
     year = {2000},
     mrnumber = {1804652},
     zbl = {0988.74031},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2000__17_6_711_0/}
}
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Demoulini, Sophia; Stuart, David M. A.; Tzavaras, Athanasios E. Construction of entropy solutions for one dimensional elastodynamics via time discretisation. Annales de l'I.H.P. Analyse non linéaire, Tome 17 (2000) no. 6, pp. 711-731. http://www.numdam.org/item/AIHPC_2000__17_6_711_0/

[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 Mathematics 50, Pitman, Boston, 1981, pp. 50- 62. | MR | Zbl

[2] Chen G.-Q., Frid H., Decay of entropy solutions of nonlinear conservation laws, Arch. Rational Mech. Anal. 146 (1999) 95-127. | MR | Zbl

[3] Dafermos C., Estimates for conservation laws with little viscosity, SIAM J. Math. Anal. 18 (1987) 409-421. | MR | Zbl

[4] Demoulini S., Young measure solutions for nonlinear evolutionary systems of mixed type, Annales de l'I.H.P., Analyse Non Linéaire 14 (1) (1997) 143-162. | EuDML | Numdam | MR | Zbl

[5] Demoulini S., Weak solutions for a class of nonlinear systems of viscoelasticity, Arch. Rat. Mech. Analysis, to appear. | MR | Zbl

[6] Demoulini S., Stuart D., Tzavaras A., A variational approximation scheme for three dimensional elastodynamics with polyconvex energy, preprint. | Zbl

[7] Diperna R., Convergence of approximate solutions to conservation laws, Arch. Rational Mech. Analysis 82 (1983) 27-70. | MR | Zbl

[8] Godlewski E., Raviart P.-A., Numerical Approximation of Hyperbolic Systems of Conservation Laws, Springer-Verlag, New York, 1996. | MR | Zbl

[9] Hörmander L., Lectures on Nonlinear Hyperbolic Differential Equations, Springer-Verlag, Berlin, 1997. | MR | Zbl

[10] Kinderlehrer D., Perdregal P., Weak convergence of integrands and the Young measure representation, SIAM J. Math. Anal. 23 (1992) 1-19. | MR | Zbl

[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. | MR | Zbl

[12] Lin P, Young measures and an application of compensated compactness to one-dimensional nonlinear elastodynamics, Trans. Amer. Math. Soc. 329 (1992) 377- 413. | MR | Zbl

[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. | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[19] Tzavaras A., Materials with internal variables and relaxation to conservation laws, Arch. Rational Mech. Anal. 146 (1999) 129-155. | MR | Zbl