A system of conservation laws with a relaxation term
(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.
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/1224361
- author
- Schroll, Achim ^{LU} ; Tveito, Aslak and Winther, Ragnar
- publishing date
- 1996
- 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}, }