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The partial differential equation $ u\sb{t}+f(u)\sb{x}=-cu$


Author: Harumi Hattori
Journal: Proc. Amer. Math. Soc. 86 (1982), 395-401
MSC: Primary 35L65; Secondary 35C05
DOI: https://doi.org/10.1090/S0002-9939-1982-0671202-3
MathSciNet review: 671202
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Abstract: Lax's solution formula for the equation $ {u_t} + f{(u)_x} = 0$ is extended to the equation $ {u_t} + f{(u)_x} = - cu$.


References [Enhancements On Off] (What's this?)

  • [1] P. D. Lax, Hyperbolic systems of conversation laws. II, Comm. Pure Appl. Math. 10 (1957), 537-566. MR 0093653 (20:176)
  • [2] -, Hyperbolic systems of conservation laws and the mathematical theory of shock waves, SIAM Regional Conf. Ser. Appl. Math., Society for Industrial and Applied Mathematics, Philadelphia, 1973. MR 0350216 (50:2709)
  • [3] T. Nishida, Global smooth solutions for the second order quasilinear wave equations with first order dissipation, unpublished, 1975.
  • [4] M. Slemrod, Instability of steady shearing flows in a nonlinear viscoelastic fluid, Arch. Rational Mech. Anal. 68 (1978), 211-225. MR 509225 (80c:76004)
  • [5] D. Shisha, Monotone approximation, Pacific J. Math. 15 (1965), 667-671. MR 0185334 (32:2802)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0671202-3
Keywords: Conservation laws, shock
Article copyright: © Copyright 1982 American Mathematical Society

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