Stability of viscous profiles: Proofs via dichotomies

Journal of Dynamics and Differential Equations

Volumn 18, Issue 1, 2006, Pages 141-195

  Beyn, Wolf Jürgen ^a   Lorenz, Jens ^b  

^a BIELEFELD UNIVERSITY   (Germany)

^b UNIVERSITY OF NEW MEXICO   (United States)

Author keywords

Stability; Viscous conservation laws; Viscous profiles; Zeromass condition

Indexed keywords

EID: 33646408119     PISSN: 10407294     EISSN: 15729222     Source Type: Journal    
DOI: 10.1007/s10884-005-9003-0     Document Type: Article

References (17)

1. Beyn, W.-J. (1990). The numerical computation of connecting orbits in dynamical systems. IMA J. Numcr. Anal. 10, 379-405.
2. Beyn, W.-J., and Lorenz, J. (1999). Stability of traveling waves: Dichotomies and eigen-value conditions on finite intervals. Numer. Fund. Anal. Optimiz. 20, 201-244.
3. Coppel, W. A. (1978). Dichotomies in Stability Theory. Springer Lecture Notes in Mathematics 629.
4. Goodman, J. (1986). Nonlinear asymptotic stability of viscous shock profiles for conservation laws. Arch. Rat. Mech. Anal. 95, 325-344.
5. Hale, J. K., and Lin, X.-B. (1986). Heteroclinic orbits for retarded functional differential equations. J. Diff. Eqns. 65, 175-202.
6. Kreiss, G., and Kreiss, H.-O. (1998). Stability of systems of viscous conservation laws. Comm. Pure Appl. Math. LI, 1397-1424.
7. Kreiss, G., Kreiss, H.-O., and Lorenz, J. (1999). On stability of conservation laws. SIAM J. Math. Anal., 20(2), 401-430.
8. Lax, P. (1973). Hyperbolic systems of conservation laws. SIAM Reg. Conf. Series 77, 1-43.
9. Liu, T.-P. (1985). Nonlinear stability of shock waves for viscous conservation laws. Mem. Am. Math. Soc. 56, v+108 328.
10. Liu, T.-P. (1997). Pointwise convergence to shock waves for the system of viscous conservation laws. Comm. Pure Appl. Math. 50, 1113-1182.
11. Mascia, C., and Zumbrun, K. (2004). Stability of large-amplitude viscous shock profiles of hyperbolic-parabolic systems.
12. Palmer, K. J. (1984). Exponential dichotomies and transversal homoclinic points. J. Diff. Eqns. 55, 225-256.
13. Sacker, R. J. (1978). Existence of dichotomies and invariant splittings for linear differential systems IV. J. Diff. Eqns. 27, 106-137.
14. Sacker, R.J., and Sell, G.R. (1978). A spectral theory for linear differential operators. J. Diff. Eqns. 27, 320-358.
15. Zumbrun, K., and Howard, P. (1998). Pointwise semigroup methods and stability of viscous shock waves. Indiana Univ. Math. J. 47, 741-871.
16. Zumbrun, K., and Howard, P. (2002). Errata to 'Pointwise semigroup methods and stability of viscous shock waves' [Indiana Univ. Math. J. 47, 741-871, 1998]
17. Indiana Univ. Math. J. 51, 1017-1021.