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


On $ L\sb 1$-contraction for systems of conservation laws

Author: Jorge G. S. Patiño
Journal: Proc. Amer. Math. Soc. 101 (1987), 465-469
MSC: Primary 35L65
MathSciNet review: 908650
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Abstract: We prove that for $ 2 \times 2$, strictly hyperbolic, genuinely nonlinear systems of conservation laws, there is no metric $ D$ such that

$\displaystyle \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$.

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PII: S 0002-9939(1987)0908650-4
Keywords: Conservation laws, decay of solutions, $ {L_1}$-dependence
Article copyright: © Copyright 1987 American Mathematical Society