Traveling-wave solutions of convection-diffusion systems in nonconservation form

SIAM Journal on Mathematical Analysis

Volumn 27, Issue 5, 1996, Pages 1286-1310

  Sainsaulieu, Lionel ^a  

^a UNIVERSITÉ PARIS EST   (France)

Author keywords

Convection diffusion systems; Hyperbolic systems in nonconservation form; Lax entropy conditions; Shock waves; Traveling waves

Indexed keywords

EID: 0030514650     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/0527071     Document Type: Article

References (17)

1. R. COURANT AND K. O. FRIEDRICHS, Supersonic Flows and Shock Waves, Wiley-Interscience, New York, 1948; reprinted by Springer-Verlag, New York, 1985.
2. L. SAINSAULIEU, A Euler system modeling vaporizing sprays, in Dynamics of Heterogeneous Combustion and Reacting Systems, Progress Series in Astronautics and Aeronautics 152, A. L. Kuhl et al., eds., American Institute of Aeronautics and Astronautics, Washington, DC, 1993, pp. 280-305.
3. P. EMBID AND M. BAER, Mathematical analysis of a two-phase model for reactive granular material, Technical report SAND88-3302, Sandia National Laboratory, Albuquerque, NM, 1989.
4. E. F. TORO, Riemann-problem based techniques for computing reactive two-phase flows, in Numerical Combustion, A. Dervieux and B. Larrouturou, eds., Lectures Notes in Phys. 351, Springer-Verlag, Heidelberg, 1989, pp. 472-481.
5. S. K. GODUNOV AND E. I. ROMENSKII, Nonstationary equations of nonlinear elasticity theory in Eulerian coordinates, Zh. Prikl. Mekh. Tekh., 6 (1972), pp. 124-144.
6. A. I. VOLPERT, The space BV and quasilinear equations, Mat. Sb., 73 (1967), pp. 225-267.
7. G. DAL MASO, P. LE FLOCH, AND F. MURAT, Definition and weak stability of a nonconservative product, J. Math. Pures Appl., to appear.
8. J.-F. COLOMBEAU, Multiplication of distributions, Bull. Amer. Math. Soc., 23 (1990), pp. 251-268.
9. J.-F. COLOMBEAU AND A. HEIBIG, Nonconservative products in bounded variation functions, SIAM J. Math. Anal., 23 (1992), pp. 941-949.
10. P. LE FLOCH, Shock waves for nonlinear hyperbolic systems in nonconservative form, preprint series 593, Institute for Mathematics and Its Applications, University of Minnesota. Minneapolis, MN, 1989.
11. P.-A. RAVIART AND L. SAINSAULIEU, A nonconservative convection-diffusion system describing spray dynamics, part 1: Solution of Riemann problem, Math. Models Methods Appl. Sci., 5 (1995), pp. 297-333.
12. A. MAJDA AND R. PEGO, Stable viscosity matrices for systems of conservation laws, J. Differential Equations, 56 (1985), pp. 229-262.
13. D. WAGNER, The existence and behavior of viscous structure for plane detonation waves, SIAM J. Math. Anal., 20 (1989), pp. 1035-1054.
14. B. L. KEYFITZ AND G. G. WARNECKE, The existence of viscous profiles and admissibility for transonic shocks, Comm. Partial Differential Equations, 16 (1991), pp. 1197-1221.
15. J. SMOLLER, Shock waves and reaction diffusion equations, in Grundlehren der mathematischen Wissenschaft 258, Springer-Verlag, New York, 1982.
16. E. GODLEWSKI AND P.-A. RAVIART, Hyperbolic Systems of Conservation Laws, Ellipses, Paris, 1991.
17. T. P. LIU, private communication, 1992.