Skip to main content
SpringerLink
Log in

Approximate Solutions to Conservation Laws Via Convective Parabolic Equations : Analytical and Numerical Results

  • Conference paper
Dynamics of Infinite Dimensional Systems

Part of the book series: NATO ASI Series ((NATO ASI F,volume 37))

  • 461 Accesses

Abstract

The porpuse of the present paper is to provide some results on the limiting behavior for the convective parabolic equation

$$ u_t + f\left( u \right)_x = \in \psi \left( u \right)_{xx} \quad x \in \mathbb{R},t \geq 0 $$
(1.1)

as the parameter ∈ goes to zero.

Partially supported by CNR-GNAFA.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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. R.J. Di Perna“Convergence of Approximate Solutions Conservation Laws” Arch. Rat. Mech. and Analysis 82 (1983), 27–70.

    Google Scholar 

  2. R.J. Di Perna“Measure-valued Solutions to Conservation Laws” Arch. Rat. Mech. and Analysis 88 (1985), 223–270.

    Article  Google Scholar 

  3. R.J. Di Perna“Compensated Compactness and General Systems of Conservation Laws”. Trans’.;AMS 292 (1985), 383–420.

    Article  MATH  Google Scholar 

  4. M.G. Crandall and A.Majda “Monotone Difference Approximations for Scalar Conservation Laws” Mathematics of Comp. 34 (1980), 1–21.

    MathSciNet  MATH  Google Scholar 

  5. J.Glimm“Solutions in the Large for Nonlinear Hyperbolic systems of Equations” Comm. Pure and Appl. Math. 18 (1965), 697–715. P.Marcati

    Google Scholar 

  6. P.Marcati “Convergence of Approximate Solutions to Scalar Conservation Laws by degenerate Diffusion” Preprint Univ.L’Aquila Dec. 85, (submitted).

    Google Scholar 

  7. F. Murat “L’injection du cône positif de H −1 dans W −1,q est compact pour tout q 2“ J. Math.pures et appl. 60 (1981), 309–322.

    Google Scholar 

  8. F. Murat “Compacitè par compensation ” Ann. Scuola Norm. Sup. Pisa 5 (1978), 489–507; 1 1981 ), 69–102.

    MathSciNet  Google Scholar 

  9. J.A.Smoller “Shock Waves and Reaction Diffusion Equations” Grundlehren der mathematischen Wissenschaften 258 Springer-Verlag, Berlin, Heidelberg, New York, Tokyo 1983.

    Google Scholar 

  10. L. Tartar “Compensated Compactness and Applications to Partial Differential Equations” Res. Notes in Math. 4 (R.J.Knops, ed) Pitman Press 1979.

    Google Scholar 

  11. L. Tartar “The Compesated Compactness Method applied to Systems of Conservation Laws”. In Systems of Nonlinear PDES. (J. Ball Ed.) D. Reidel Publishing Co.1983

    Google Scholar 

  12. S. Osher and J. Ralston “L Stability of Travelling Waves with Applications to Convective Porous Media Flow”. Comm. Pure and Appl. Math. 35 (1982), 737–749

    MathSciNet  MATH  Google Scholar 

  13. A.I. Vol’ pert and S.I.Hudjaev“Cauchy Problem, for Degenerate Second Order Quasilinear Parabolic Equations”. Math. USSR Sbornik 7 (1969)365–387.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Pure and Appl. Mathematics, University of L’Aquila, 67100, L’Aquila, Italy

    Pierangelo Marcati

Authors
  1. Pierangelo Marcati
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics, Michigan State University, 48824-1027, East Lansing, MI, USA

    Shui-Nee Chow

  2. Division of Applied Mathematics, Brown University, 02912, Providence, RI, USA

    Jack K. Hale

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Marcati, P. (1987). Approximate Solutions to Conservation Laws Via Convective Parabolic Equations : Analytical and Numerical Results. In: Chow, SN., Hale, J.K. (eds) Dynamics of Infinite Dimensional Systems. NATO ASI Series, vol 37. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-86458-2_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-86458-2_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-86460-5

  • Online ISBN: 978-3-642-86458-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation