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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Stability of viscous scalar shock fronts in several dimensions
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by Jonathan Goodman PDF
Trans. Amer. Math. Soc. 311 (1989), 683-695 Request permission


We prove nonlinear stability of planar shock front solutions for viscous scalar conservation laws in two or more space dimensions. The proof uses the "integrated equation" and an effective equation for the motion of the front itself. We derive energy estimates that balance terms from the integrated equation with terms from the front motion equation.
    N. Dunford and J. T. Schwartz, Linear operators, Wiley, New York, 1958.
  • Gerald B. Folland, Introduction to partial differential equations, Mathematical Notes, Princeton University Press, Princeton, N.J., 1976. Preliminary informal notes of university courses and seminars in mathematics. MR 0599578
  • I. M. Gel′fand, Some problems in the theory of quasi-linear equations, Uspehi Mat. Nauk 14 (1959), no. 2 (86), 87–158 (Russian). MR 0110868
  • Jonathan Goodman, Nonlinear asymptotic stability of viscous shock profiles for conservation laws, Arch. Rational Mech. Anal. 95 (1986), no. 4, 325–344. MR 853782, DOI 10.1007/BF00276840
  • A. M. Il’ in and O. A. Oleinik, Behavior or the solution of the Cauchy problem for certain quasilinear equations for unbounded increase of the time, Amer. Math. Soc. Transl. (2) 42 (1964), 19-23.
  • Shuichi Kawashima and Akitaka Matsumura, Asymptotic stability of traveling wave solutions of systems for one-dimensional gas motion, Comm. Math. Phys. 101 (1985), no. 1, 97–127. MR 814544
  • Tai-Ping Liu, Nonlinear stability of shock waves for viscous conservation laws, Mem. Amer. Math. Soc. 56 (1985), no. 328, v+108. MR 791863, DOI 10.1090/memo/0328
  • G. Ludford (Ed.), Reacting flows: Combustion and chemical reators, Proc. ’85 AMS/SIAM Summer Seminar in Appl. Math., Cornell Univ., Amer. Math. Soc., Providence, R.I., 1986.
  • D. H. Sattinger, On the stability of waves of nonlinear parabolic systems, Advances in Math. 22 (1976), no. 3, 312–355. MR 435602, DOI 10.1016/0001-8708(76)90098-0
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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 311 (1989), 683-695
  • MSC: Primary 35K30; Secondary 35B35, 35L67
  • DOI:
  • MathSciNet review: 978372