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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The partial differential equation $u_{t}+f(u)_{x}=-cu$
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by Harumi Hattori PDF
Proc. Amer. Math. Soc. 86 (1982), 395-401 Request permission

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
  • P. D. Lax, Hyperbolic systems of conservation laws. II, Comm. Pure Appl. Math. 10 (1957), 537–566. MR 93653, DOI 10.1002/cpa.3160100406
  • Peter D. Lax, Hyperbolic systems of conservation laws and the mathematical theory of shock waves, Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, No. 11, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1973. MR 0350216
  • T. Nishida, Global smooth solutions for the second order quasilinear wave equations with first order dissipation, unpublished, 1975.
  • M. Slemrod, Instability of steady shearing flows in a nonlinear viscoelastic fluid, Arch. Rational Mech. Anal. 68 (1978), no.Β 3, 211–225. MR 509225, DOI 10.1007/BF00247740
  • O. Shisha, Monotone approximation, Pacific J. Math. 15 (1965), 667–671. MR 185334, DOI 10.2140/pjm.1965.15.667
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • 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