Asymptotic Behavior of Hyperbolic Boundary Value Problems with Relaxation Term

Kress, Wendy

doi:10.1007/978-3-0348-8372-6_17

Wendy Kress¹⁰

Part of the book series: ISNM International Series of Numerical Mathematics ((ISNM,volume 141))

534 Accesses

Abstract

A first order hyperbolic 2 x 2 relaxation system in one space dimension is considered. The behavior of the system with general boundary conditions as the relaxation parameter tends to zero is investigated. It is shown that under certain conditions the solutions converge to the entropy solution of the resulting nonlinear hyperbolic equation u_t+ f (u)_x= 0.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Chapter: USD 29.95; Price excludes VAT (USA)

eBook: USD 84.99; Price excludes VAT (USA)

Softcover Book: USD 109.99; Price excludes VAT (USA)

Hardcover Book: USD 109.99; Price excludes VAT (USA)

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

References

C. Bardos, A.Y. Leroux, J.C. Nedelec. First order quasilinear equations with boundary conditions. Comm. in PDEs 4(9) (1979), 1017–1034.
Article MathSciNet MATH Google Scholar
E. Giusti. Minimal surfaces and functions of bounded variation. Birkhäuser, 1984.
Google Scholar
Shi Jin, Xin Zhouping. The relaxation schemes for systems of conservation laws in arbitrary space dimensions. Comm. in Pure and Appl. Math. 48 (1995), 235–277.
MATH Google Scholar
M. A. Katsoulakis, A. E. Tzavaras. Contractive relaxation systems and the scalar multidimensional conservation law. Comm. in PDEs 22 (1997), 195–233.
MathSciNet MATH Google Scholar
W. Kress. Asymptotisches Verhalten von hyperbolischen Randwertproblemen mit Relaxationsterm. Diplomthesis. Heidelberg, 1999.
Google Scholar
S.N. Kruskov. First order quasilinear equations with several independent variables. Math. USSR Sbornik 10 (1970), 217–243.
Article Google Scholar
A. Nonni, A. Omrane, J.P. Vila. Boundary conditions for scalar conservation laws from a kinetic point of view. J. Statist. Phys. 94(5–6) (1999), 779–804.
MathSciNet Google Scholar
Wang Wei-Cheng, Xin Zhouping. Asymptotic limit of the initial boundary value problem for conservation laws with relaxational extensions. Comm. in Pure and Appl. Math. 51(5) (1998), 505–535.
MathSciNet MATH Google Scholar

Download references

Author information

Authors and Affiliations

Department of Scientific Computing, University of Uppsala, P.O.Box 120, Uppsala, SE-75104, Sweden
Wendy Kress

Authors

Wendy Kress
View author publications
You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22-26, Leipzig, 04103, Germany
Heinrich Freistühler
Institute of Analysis and Numerical Mathematics, Otto-von-Guericke-University, PSF 4120, Magdeburg, 39106, Germany
Gerald Warnecke

Rights and permissions

Reprints and permissions

Copyright information

About this paper

Cite this paper

Kress, W. (2001). Asymptotic Behavior of Hyperbolic Boundary Value Problems with Relaxation Term. In: Freistühler, H., Warnecke, G. (eds) Hyperbolic Problems: Theory, Numerics, Applications. ISNM International Series of Numerical Mathematics, vol 141. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8372-6_17

Download citation

DOI: https://doi.org/10.1007/978-3-0348-8372-6_17
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9538-5
Online ISBN: 978-3-0348-8372-6
eBook Packages: Springer Book Archive

Publish with us

Policies and ethics