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- W2000684856 abstract "Let $(ast )$ [ quad {u_t} + F{(u)_x} = 0] be any $2 times 2$ system of conservation laws satisfying certain generic assumptions on $F$ in a neighborhood $mathcal {N}$ of $u$-space. We prove that for every nondegenerate metric $D$ on $u$-space there exists states ${u_1}$ and ${u_2}$ in $mathcal {N}$ such that $int _{ - infty }^infty {D(u(x,t),{u_1});dx}$ is a strictly increasing function of $t$ in a neighborhood of $t = 0$, where $u$ is the admissible solution of $( ast )$ with initial data [ u(x,0) = left { {begin {array}{*{20}{c}} {{u_1},} hfill & {x leqslant 0,} hfill {{u_2},} hfill & {0 < x < 1,} hfill {{u_1},} hfill & {x geqslant 1.} hfill end {array} } right .] This contrasts with the case of a scalar equation in which $int _{ - infty }^infty {D(u(x,t),v(x,t));dx}$ is a decreasing function of $t$ for all admissible solution pairs $u$ and $v$ when $D$ is taken to be the absolute value norm." @default.
- W2000684856 created "2016-06-24" @default.
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- W2000684856 date "1985-02-01" @default.
- W2000684856 modified "2023-10-14" @default.
- W2000684856 title "No $Lsb 1$-contractive metrics for systems of conservation laws" @default.
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- W2000684856 doi "https://doi.org/10.1090/s0002-9947-1985-0776388-5" @default.
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