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A system of conservation laws with a relaxation term

Schroll, Achim LU ; Tveito, Aslak and Winther, Ragnar (1996) 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
; and
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
Hyperbolic problems: theory, numerics, applications
pages
494 pages
publisher
World Scientific Publishing
ISBN
981-02-2441-9
language
English
LU publication?
no
id
1cf0aa97-37fd-401b-a4d9-722376af4005 (old id 1224361)
date added to LUP
2016-04-04 12:01:01
date last changed
2021-01-25 10:54:26
@inproceedings{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}},
  booktitle    = {{Hyperbolic problems: theory, numerics, applications}},
  isbn         = {{981-02-2441-9}},
  language     = {{eng}},
  pages        = {{431--439}},
  publisher    = {{World Scientific Publishing}},
  title        = {{A system of conservation laws with a relaxation term}},
  year         = {{1996}},
}