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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

Nonlinear stability of shock waves for viscous conservation laws


Author: Tai-ping Liu
Journal: Bull. Amer. Math. Soc. 12 (1985), 233-236
MSC (1980): Primary 35K55, 76N10; Secondary 35B40, 35L65
MathSciNet review: 776475
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  • 1. Jonathan Goodman, Nonlinear asymptotic stability of viscous shock profiles for conservation laws, Arch. Rational Mech. Anal. 95 (1986), no. 4, 325–344. MR 853782 (88b:35127), http://dx.doi.org/10.1007/BF00276840
  • 2. Eberhard Hopf, The partial differential equation 𝑢_{𝑡}+𝑢𝑢ₓ=𝜇𝑢ₓₓ, Comm. Pure Appl. Math. 3 (1950), 201–230. MR 0047234 (13,846c)
  • 3. A. M. Il′in and O. A. Oleĭnik, Asymptotic behavior of solutions of the Cauchy problem for some quasi-linear equations for large values of the time, Mat. Sb. (N.S.) 51 (93) (1960), 191–216 (Russian). MR 0120469 (22 #11222)
  • 4. S. Kawashima and A. Matzumura, Asymptotic stability of traveling wave solutions of system for one-dimensional gas motion.
  • 5. P. D. Lax, Hyperbolic systems of conservation laws. II, Comm. Pure Appl. Math. 10 (1957), 537–566. MR 0093653 (20 #176)
  • 6. Tai-Ping Liu, Linear and nonlinear large-time behavior of solutions of general systems of hyperbolic conservation laws, Comm. Pure Appl. Math. 30 (1977), no. 6, 767–796. MR 0499781 (58 #17556)
  • 7. A. Matzumura and K. Nishihara, On a stability of traveling wave solutions of a one-dimensional model system of compressible viscous gas (preprint).

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Additional Information

DOI: http://dx.doi.org/10.1090/S0273-0979-1985-15356-X
PII: S 0273-0979(1985)15356-X