References
R. Courant & K. Friedrichs, Supersonic Flow and Shock Waves (1948), Springer Verlag, New York.
L. Foy, “Steady state solutions of conservation laws with viscosity terms,” Comm. Pure Appl. Math. 17 (1964), pp. 177–188.
A. Friedman, Partial Differential Equations of Parabolic Type (1964), Prentice-Hall, Englewood Cliffs, New Jersey.
J. Goodman & A. Majda, “The validity of the modified equation for nonlinear shock waves,” submitted to J. Comp. Phys.
D. Henry, “Geometric Theory of Semilinear Parabolic Equations,” Lecture Notes in Math. No. 840 (1981), Springer-Verlag, New York.
A. M. Il'in & O. A. Oleinik, “Behavior of the solution of the Cauchy problem for certain quasilinear equations for unbounded increase of the time,” Amer. Math. Soc. Translations, Ser. 2, 42 (1964), pp. 19–23, Amer. Math. Soc., Providence, R.I.
T. Kato, “The Cauchy problem for quasilinear symmetric hyperbolic systems,” Arch. Rational Mech. 58 (1975), pp. 181–205.
A. Kelley, “Stability of the center stable manifold,” J. Math. Anal Appl. 18 (1967), pp. 336–344.
N. Kopell & L. Howard, “Bifurcations and trajectories joining critical points,” Adv. Math. 18 (1975), pp. 306–358.
L. D. Landau & E. M. Lifschitz, Fluid Mechanics (1959), Pergamon Press, London.
P. Lax, Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves (1973), Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania.
A. Majda & R. Pego, “Stable viscosity matrices for systems of conservation laws,” Math. Res. Cen. Technical Summary Report 2491, Univ. of SWisc., Madison, Wi.
R. Pego, “Linearized stability of extreme shock profiles for systems of conservation laws with viscosity,” Math. Res. Cen. Technical Summary Report 2457, Univ. of Wisc., Madison, Wi.
D. Sattinger, “n the stability of waves of nonlinear parabolic systems,” Adv. Math. 22 (1976), pp. 312–355.
Author information
Authors and Affiliations
Additional information
Communicated by C. Dafermos
Rights and permissions
About this article
Cite this article
Goodman, J. Nonlinear asymptotic stability of viscous shock profiles for conservation laws. Arch. Rational Mech. Anal. 95, 325–344 (1986). https://doi.org/10.1007/BF00276840
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00276840