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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


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
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?)

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  • [2] Peter D. Lax, Hyperbolic systems of conservation laws and the mathematical theory of shock waves, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1973. Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, No. 11. 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• [3] T. Nishida, Global smooth solutions for the second order quasilinear wave equations with first order dissipation, unpublished, 1975.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), no. 3, 211–225. MR 509225 (80c:76004),
  • [5] O. Shisha, Monotone approximation, Pacific J. Math. 15 (1965), 667–671. MR 0185334 (32 #2802)

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Additional Information

PII: S 0002-9939(1982)0671202-3
Keywords: Conservation laws, shock
Article copyright: © Copyright 1982 American Mathematical Society