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A system of conservation laws with a relaxation term

Schroll, Achim LU ; Tveito, Aslak and Winther, Ragnar (1996) In Hyperbolic problems: theory, numerics, applications p.431-439
Abstract
The Cauchy problem for the following system of conservation laws with relaxation time $delta$ is discussed: $(ast)$ $(u+v)_t+f(u)_x=0$, $delta v_t=A(u)-v$. A theorem on the well-posedness of the problem is given in the class of functions with bounded total variation. Then the behaviour of solutions to $(ast)$ as $delta o 0$ is treated and convergence of a certain finite-difference scheme to the solution of an equilibrium model $(astast)$ $(w+A(w))_t+f(w)_x=0$ is proved. It is shown that the $L_1$-difference between an equilibrium solution and a nonequilibrium one is bounded by $O(delta^{1/3})$. Detailed proofs are given in related papers by the authors.
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author
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
in
Hyperbolic problems: theory, numerics, applications
pages
494 pages
publisher
World Scientific
ISBN
981-02-2441-9
language
English
LU publication?
no
id
1cf0aa97-37fd-401b-a4d9-722376af4005 (old id 1224361)
date added to LUP
2008-09-02 11:37:28
date last changed
2016-09-29 10:14:50
@misc{1cf0aa97-37fd-401b-a4d9-722376af4005,
  abstract     = {The Cauchy problem for the following system of conservation laws with relaxation time $delta$ is discussed: $(ast)$ $(u+v)_t+f(u)_x=0$, $delta v_t=A(u)-v$. A theorem on the well-posedness of the problem is given in the class of functions with bounded total variation. Then the behaviour of solutions to $(ast)$ as $delta	o 0$ is treated and convergence of a certain finite-difference scheme to the solution of an equilibrium model $(astast)$ $(w+A(w))_t+f(w)_x=0$ is proved. It is shown that the $L_1$-difference between an equilibrium solution and a nonequilibrium one is bounded by $O(delta^{1/3})$. Detailed proofs are given in related papers by the authors.},
  author       = {Schroll, Achim and Tveito, Aslak and Winther, Ragnar},
  isbn         = {981-02-2441-9},
  language     = {eng},
  pages        = {431--439},
  publisher    = {ARRAY(0x9000248)},
  series       = {Hyperbolic problems: theory, numerics, applications},
  title        = {A system of conservation laws with a relaxation term},
  year         = {1996},
}