Skip to main content

Large Time Asymptotics in Contaminant Transport in Porous Media with Variable Diffusion

  • Conference paper
Hyperbolic Problems: Theory, Numerics, Applications

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 140))

  • 493 Accesses

Abstract

This paper is devoted to the study of the large time behavior of solutions of the equations modelling contaminant transport in porous media with variable diffusion for integrable initial data.

The goal of this work is to study the large time behavior of a reactive solute which undergoes equilibrium adsorption in a porous medium with variable diffusion.

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

Access this chapter

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
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover 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. A. Carpio.Large time behaviour in some convection-diffusion equations.Ann. Sc. Norm. Sup. Pisa, serie IV, XXIII, Fasc. 3, (1996), 551–574.

    MathSciNet  Google Scholar 

  2. C. N. Dawson, C. J. Van Duijn and R. E. Grundy.Asymptotic profiles with finite mass in one-dimensional contaminant transport through porous media: The fast reaction case.Quart. J. Mech. Appl. Math., 47, (1994), 69–106.

    Article  MathSciNet  MATH  Google Scholar 

  3. C. N. Dawson, C. J. Van Duijn and R. E. Grundy.Large time asymptotics in contaminant transport in porous media. SIAM J. Appl. Math. 56, 4, (1996), 965–993.

    Article  MathSciNet  MATH  Google Scholar 

  4. G. Duro.Asymptotic profiles in contaminant transport in porous media with variable diffusion.To appear in Adv Math, Sci. and Appl., 11, 2 (2001).

    MathSciNet  Google Scholar 

  5. G. Duro and A. Carpio.Asymptotic profiles in convection-diffusion with variable diffusion.To appear in Nonlinear Anal., (2001).

    Google Scholar 

  6. G. Duro and E. Zuazua.Large time behavior for convection-diffusion equations in IR N with asymptotically constant diffusionComm P D E, 24 (7&8), (1999), 1283–1340.

    Article  MathSciNet  MATH  Google Scholar 

  7. G. Duro and E. Zuazua.Large time behavior for convection-diffusion equations with periodic coefficients.Jour. Diff. Equations, 167, 275–315 (2000).

    Article  MathSciNet  MATH  Google Scholar 

  8. M. Escobedo, J.L. Vázquez and E. Zuazua.Asymptotic behavior and source-type solutions for a diffusion-convectionequation. Archives Rat. Mech. Anal., 124, (1993), 43–65.

    MATH  Google Scholar 

  9. M. Escobedo and E. Zuazua.Large time behavior for solutions ofaconvection dif fusion equation in IR N .J. Funct. Anal., 100 (1), (1991), 119–162.

    Article  MathSciNet  MATH  Google Scholar 

  10. P. Lax. Hyperbolic systems of conservation laws.II, Comm Pure Appl. Maths., 10, (1957), 537–566.

    MathSciNet  MATH  Google Scholar 

  11. T. P. Liu and M. Pierre.Source solutions andasymptoticbehaviour in conservation laws.Jour. Diff. Equations, 51 (1984), 419–441.

    Article  MathSciNet  MATH  Google Scholar 

  12. P. Li and S. T. Yau.On the parabolic Kernel of the Schrödinger operator.Acta Mathematica, 156, (1986), 153–201.

    Article  MathSciNet  Google Scholar 

  13. M. Murata. Large timeasymptotics for fundamental solutions of diffusion equations.Tohoku Mathematical Journal, 37, (1985), 151–195.

    Article  MathSciNet  Google Scholar 

  14. J. Simon.Compact sets in the space LP (0 T; B).Annali Mat. Pura Appl., CXLVI, (1987), 65–96.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer Basel AG

About this paper

Cite this paper

Duro, G., Zuazua, E. (2001). Large Time Asymptotics in Contaminant Transport in Porous Media with Variable Diffusion. In: Freistühler, H., Warnecke, G. (eds) Hyperbolic Problems: Theory, Numerics, Applications. International Series of Numerical Mathematics, vol 140. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8370-2_33

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-8370-2_33

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9537-8

  • Online ISBN: 978-3-0348-8370-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics