Skip to main content
Log in

Asymptotic behaviour of solutions of a nonlinear diffusion equation

  • Published:
Archive for Rational Mechanics and Analysis Aims and scope Submit manuscript

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Aronson, D.G., Regularity properties of flows through porous media, SIAM J. Appl. Math., 17, 461–467 (1969).

    Google Scholar 

  2. Atkinson, F.V. & L.A. Peletier, Similarity solutions of the nonlinear diffusion equation, Arch. Rational Mech. Anal., 54, 373–392 (1974).

    Google Scholar 

  3. Duyn, C.J. van & L.A. Peletier, A class of similarity solutions of the nonlinear diffusion equation, Nonlinear Analysis, Theory, Methods & Applications, 1, 223–233 (1977).

    Google Scholar 

  4. Gilding, B. H., Stabilization of flows through porous media, SIAM J. Appl. Math., (to appear).

  5. Kamenomostskaya, S., Asymptotic behaviour of the solution of the filtration equation, Israel J. Math., 14, 76–87 (1973).

    Google Scholar 

  6. Oleinik, O.A. & S.N. Kruzhkov, Quasi-linear second-order parabolic equations with many independent variables, Uspehi Mat. Nauk., 16, 115–155 (1961) = Russian Math. Surveys, 16, 105–146 (1961).

    Google Scholar 

  7. Peletier, L.A., Asymptotic behaviour of temperature profiles of a class of non-linear heat conduction problems, Quart. J. Mech. Appl. Math., 23, 441–447 (1970).

    Google Scholar 

  8. Peletier, L. A., Asymptotic behaviour of solutions of the porous media equation, SIAM J. Appl. Math., 21, 542–551 (1971).

    Google Scholar 

  9. Serrin, J., Asymptotic behaviour of velocity profiles in the Prandtl boundary layer theory, Proc. Ray. Soc., A299, 491–507 (1967).

    Google Scholar 

  10. Serrin, J., private communication.

  11. Serrin, J., Gradient estimates for solutions of nonlinear elliptic and parabolic equations, in Contributions to Nonlinear Functional Analysis, edited by E. H. Zarantonello, Academic Press, New York (1971).

    Google Scholar 

  12. Shampine, L.F., Concentration dependent diffusion I, Quart. Appl. Math., 30, 441–452 (1973).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by J. Serrin

Rights and permissions

Reprints and permissions

About this article

Cite this article

van Duyn, C.J., Peletier, L.A. Asymptotic behaviour of solutions of a nonlinear diffusion equation. Arch. Rational Mech. Anal. 65, 363–377 (1977). https://doi.org/10.1007/BF00250433

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00250433

Keywords

Navigation