On $L_ 1$-contraction for systems of conservation laws
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- by Jorge G. S. Patiño PDF
- Proc. Amer. Math. Soc. 101 (1987), 465-469 Request permission
Abstract:
We prove that for $2 \times 2$, strictly hyperbolic, genuinely nonlinear systems of conservation laws, there is no metric $D$ such that \[ \int _{ - \infty }^\infty {D(u(x,t),c)dx} \] is a nonincreasing function of time for every weak solution $u,{u_0}( \pm \infty ) = c$.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
- Blake Temple, No $L_1$-contractive metrics for systems of conservation laws, Trans. Amer. Math. Soc. 288 (1985), no. 2, 471–480. MR 776388, DOI 10.1090/S0002-9947-1985-0776388-5
- Blake Temple, Decay with a rate for noncompactly supported solutions of conservation laws, Trans. Amer. Math. Soc. 298 (1986), no. 1, 43–82. MR 857433, DOI 10.1090/S0002-9947-1986-0857433-6
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 101 (1987), 465-469
- MSC: Primary 35L65
- DOI: https://doi.org/10.1090/S0002-9939-1987-0908650-4
- MathSciNet review: 908650