Nonlinear stability with decay rate for traveling wave solutions of a hyperbolic system with relaxation

Journal of Differential Equations

Volumn 130, Issue 1, 1996, Pages 36-58

  Zingano, Paulo R ^a  

^a FEDERAL UNIVERSITY OF RIO GRANDE DO SUL   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030239584     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1996.0131     Document Type: Article

References (11)

1. 1. J. Goodman, Nonlinear asymptotic stability of viscous shock profiles for conservation laws, Arch. Rational Mech. Appl. 95 (1986), 325-344.
2. 2. S. Kawashima and A. Matsumura, Asymptotic stability of traveling wave solutions of systems for one-dimensional gas motion, Comm. Math. Phys. 101 (1985), 97-127.
3. 3. P. D. Lax, "Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves," SIAM, Philadelphia, 1973.
4. 4. M. J. Lighthill and G. B. Whitham, On kinematic waves: I. Flood movement in long rivers; II. Theory of traffic flow on long crowded roads, Proc. Roy. Soc. A 229 (1955), 281-345.
5. 5. T. P. Liu, Hyperbolic Conservation Laws with Relaxation, Comm. Math. Phys. 108 (1987), 153-175.
6. 6. O. A. Oleinik, Uniqueness and stability of the generalized solution of the Cauchy problem for a quasi-linear equation, Amer. Math. Soc. Transl. 14 (1959), 165-170.
7. 7. M. Renardy, W. J. Hrusa, and J. A. Nohel, "Mathematical Problems in Viscoelasticity," Wiley, New York, 1987.
8. 8. P. I. Richards, Shock waves on the highway, Oper. Res. 4 (1956), 42-51.
9. 9. W. G. Vincenti and C. H. Kruger Jr., "Introduction to Physical Gas Dynamics," Kriege, Malabar, 1986.
10. 10. G. B. Whitham, "Linear and Nonlinear Waves," Wiley, New York, 1974.
11. 11. P. R. Zingano, "Nonlinear Stability Analysis with Decay Rates for Two Classes of Waves," Ph.D. dissertation, New York University, 1990.