BV solutions and relaxation limit for a model in viscoelasticity

Royal Society of Edinburgh - Proceedings A

Volumn 128, Issue 4, 1998, Pages 775-795

  Luo, Tao ^a,b   Natalini, Roberto ^a  

^a CNR   (Italy)

^b INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001016446     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0308210500021776     Document Type: Article

References (23)

1. D. Aregba-Driollet and R. Natalini. Convergence of relaxation schemes for conservation laws. Appl. Anal. 61 (1996), 163-93.
2. T. Chang and L. Hsiao. The Riemann Problem and Interaction of Waves in Gas Dynamics, Pitman Monographs and Surveys in Pure and Applied Mathematics 41 (Harlow: Longman Scientific and Technical, 1989).
3. G.-Q. Chen and T. P. Liu. Zero relaxation and dissipation limits for hyperbolic conservation laws. Comm. Pure Appl. Math. 46 (1993), 755-81.
4. G.-C. Chen, C. Levermore and T. P. Liu. Hyperbolic conservation laws with stiff relaxation terms and entropy. Comm. Pure Appl. Math. 47 (1994), 787-830.
5. G. Crasta and B. Piccoli. Viscosity solutions and uniqueness for systems of inhomogeneous balance laws. Discrete Contin. Dynam. Systems 3 (1997), 477-502.
6. C. M. Dafermos and L. Hsiao. Hyperbolic systems of balance laws with inhomogeneity and dissipation. Indiana Univ. Math. J. 31 (1982), 471-91.
7. J. Glimm. Solutions in the large for nonlinear hyperbolic systems of equations. Comm. Pure Appl. Math. 18 (1965), 697-715.
8. t + (σ - μf(u)) = 0. Arch. Rational Mech. Anal. 82 (1983), 87-108.
9. B. Hanouzet and R. Natalini. Weakly coupled systems of quasilinear hyperbolic equations. Differential Integral Equations. 9 (1996), 1272-92.
10. B. Hanouzet, R. Natalini and A. Tasei. On the Chapman-Jouguet limit for a combustion model. SIAM J. Math. Anal. (in press).
11. L. Hsiao. Quasilinear hyperbolic systems and dissipative mechanisms (Singapore: World Scientific, 1998).
12. S. Jin and Z. Xin. The relaxation schemes for systems of conservation laws in arbitrary space dimensions. Comm. Pure Appl. Math. 48 (1995), 235-76.
13. P. D. Lax. Shock waves and entropy. In Contributions to nonlinear functional analysis, ed. E. Zarantonello, 603-34 (New York: Academic Press, 1971).
14. T. P. Liu. Quasilinear hyperbolic systems. Comm. Math. Phys. 68 (1979), 141-72.
15. T. P. Liu. Hyperbolic conservation laws with relaxation. Comm. Math. Phys. 108 (1987), 153-75.
16. R. Natalini. Convergence to equilibrium for the relaxation approximation of conservation laws. Comm. Pure Appl. Math. 49 (1996), 795-823.
17. R. Natalini. A discrete kinetic approximation of entropy solutions to multidimensional scalar conservation laws (Preprint IAC, Quaderno n.9, 1996).
18. H. J. Schroll, A. Tveito and R. Winther. An error bound for a finite difference scheme applied to a stiff system of conservation laws. SIAM J. Numer. Anal. 34 (1997), 1152-66.
19. D. Serre. Systèmes de lois de conservation I (Paris: Diderot, 1996).
20. J. Smoller. Shock waves and reaction-diffusion systems (New York: Springer, 1983).
21. L. Tartar. Compensated compactness and applications to partial differential equations. In Research notes in Mathematics. Nonlinear Analysis and Mechanics: Heriot-Watt Symposium, Vol. 4, ed. R. J. Knops, 136-212 (New York: Pitman, 1979).
22. A. Tveito and R. Winther. On the rate of convergence to equilibrium for a system of conservation laws including a relaxation term. SIAM J. Math. Anal. 28 (1997), 136-61.
23. J. Whitham. Linear and nonlinear waves (New York: Wiley, 1974).