The partial differential equation $u_{t}+f(u)_{x}=-cu$
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- by Harumi Hattori
- Proc. Amer. Math. Soc. 86 (1982), 395-401
- DOI: https://doi.org/10.1090/S0002-9939-1982-0671202-3
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Abstract:
Laxβs solution formula for the equation ${u_t} + f{(u)_x} = 0$ is extended to the equation ${u_t} + f{(u)_x} = - cu$.References
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- 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T. Nishida, Global smooth solutions for the second order quasilinear wave equations with first order dissipation, unpublished, 1975.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, 211β225. MR 509225, DOI 10.1007/BF00247740
- O. Shisha, Monotone approximation, Pacific J. Math. 15 (1965), 667β671. MR 185334, DOI 10.2140/pjm.1965.15.667
Bibliographic 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