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Nonlinear asymptotic stability of viscous shock profiles for conservation laws

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References

  1. R. Courant & K. Friedrichs, Supersonic Flow and Shock Waves (1948), Springer Verlag, New York.

    Google Scholar 

  2. L. Foy, “Steady state solutions of conservation laws with viscosity terms,” Comm. Pure Appl. Math. 17 (1964), pp. 177–188.

    Google Scholar 

  3. A. Friedman, Partial Differential Equations of Parabolic Type (1964), Prentice-Hall, Englewood Cliffs, New Jersey.

    Google Scholar 

  4. J. Goodman & A. Majda, “The validity of the modified equation for nonlinear shock waves,” submitted to J. Comp. Phys.

  5. D. Henry, “Geometric Theory of Semilinear Parabolic Equations,” Lecture Notes in Math. No. 840 (1981), Springer-Verlag, New York.

    Google Scholar 

  6. 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.

    Google Scholar 

  7. T. Kato, “The Cauchy problem for quasilinear symmetric hyperbolic systems,” Arch. Rational Mech. 58 (1975), pp. 181–205.

    Google Scholar 

  8. A. Kelley, “Stability of the center stable manifold,” J. Math. Anal Appl. 18 (1967), pp. 336–344.

    Google Scholar 

  9. N. Kopell & L. Howard, “Bifurcations and trajectories joining critical points,” Adv. Math. 18 (1975), pp. 306–358.

    Google Scholar 

  10. L. D. Landau & E. M. Lifschitz, Fluid Mechanics (1959), Pergamon Press, London.

    Google Scholar 

  11. P. Lax, Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves (1973), Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania.

  12. A. Majda & R. Pego, “Stable viscosity matrices for systems of conservation laws,” Math. Res. Cen. Technical Summary Report 2491, Univ. of SWisc., Madison, Wi.

  13. 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.

  14. D. Sattinger, “n the stability of waves of nonlinear parabolic systems,” Adv. Math. 22 (1976), pp. 312–355.

    Google Scholar 

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  1. Courant Institute of Mathematical Sciences, New York University, USA

    Jonathan Goodman

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  1. Jonathan Goodman
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Communicated by C. Dafermos

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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

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  • DOI: https://doi.org/10.1007/BF00276840

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