Skip to main content
SpringerLink
Log in

Multi-dimensional Stability of Propagating Phase Boundaries

  • Conference paper
Hyperbolic Problems: Theory, Numerics, Applications

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 129))

  • 616 Accesses

Abstract

The paper addresses the multi-dimensional stability of propagating phase boundaries in real fluids, from a viewpoint similar to Majda’s concerning classical discontinuities. For planar boundaries, a Lopatinski condition is derived and shown to be satisfied in the inviscid case. Some surface waves prevent the uniform Lopatinski condition to be satisfied though. Then it is shown that, for weakly dissipative phase boundaries, the surface waves are stabilized and the uniform Lopatinsky condition is satisfied.

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)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. Benzoni-Gavage, Stability of multi-dimensional phase transitions in a van der Waals fluid, Nonlinear Anal., 31 (1–2) (1998), 243–263.

    Article  MathSciNet  MATH  Google Scholar 

  2. S. Benzoni-Gavage, Stability of subsonic planar phase transitions in a van der Waals fluid, Preprint ENS Lyon 221 (1998).

    Google Scholar 

  3. H. Freistühler, The Persistence of Ideal Shock Waves, Appl. Math. Lett., 7(6) (1994), 7–11.

    Article  MathSciNet  Google Scholar 

  4. H.-O. Kreiss, Initial boundary value problems for hyperbolic systems, Comm. Pure and Applied Maths, 23 (1970), 277–298.

    Article  MathSciNet  Google Scholar 

  5. A. Majda, Compressible fluid flow and systems of conservation laws in several space variables, Springer-Verlag, Berlin, 1984.

    Book  MATH  Google Scholar 

  6. M. Slemrod, Admissibility criteria for propagating phase boundaries in a van der Waals fluid, Arch. Rational Mech. Anal, 81 (1983), 301–315.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. ENS Lyon, UMPA, 46, allée d’Italie, F-69364, Lyon Cedex 07, France

    Sylvie Benzoni

Authors
  1. Sylvie Benzoni
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Seminar for Applied Mathematics, ETH Zentrum, 8092, Zürich, Switzerland

    Michael Fey  & Rolf Jeltsch  & 

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer Basel AG

About this paper

Cite this paper

Benzoni, S. (1999). Multi-dimensional Stability of Propagating Phase Boundaries. In: Fey, M., Jeltsch, R. (eds) Hyperbolic Problems: Theory, Numerics, Applications. International Series of Numerical Mathematics, vol 129. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8720-5_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-8720-5_5

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9742-6

  • Online ISBN: 978-3-0348-8720-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation