Skip to main content
SpringerLink
Log in

Nonnegative solutions of a fourth-order nonlinear degenerate parabolic 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

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. F. Bernis, Nonlinear parabolic equations arising in semiconductor and viscous droplets models, W.-M. Ni, L. A. Peletier & J. Serrin, editors, Birkhäuser, Boston (1992), 77–88.

    Google Scholar 

  2. F. Bernis & A. Friedman, Higher order nonlinear degenerate parabolic equations, J. Differential Equations 83 (1990), 179–206.

    Google Scholar 

  3. F. Bernis, L. A. Peletier & S. M. Williams, Source type solutions of a fourth order nonlinear degenerate parabolic equation, Nonlinear Analysis T. M. A. 18 (1992), 217–233.

    Google Scholar 

  4. A. L. Bertozzi, M. P. Brenner, T. F. Dupont & L. P. Kadanoff, Singularities and similarities in interface flows, Trends and perspectives in Applied Mathematics. L. Sirovich, editor, Springer-Verlag, Berlin (1994), 155–208.

    Google Scholar 

  5. S. Boatto, L. P. Kadanoff & P. Olla, Travelling wave solutions to thin film equations, Phys. Rev. E 48 (1993), 4423–4431.

    Google Scholar 

  6. A. A. Lacey, The motion with slip of a thin viscous droplet over a solid surface, Stud. Appl. Math. 67 (1982) 217–230.

    Google Scholar 

  7. S. H. Davis, E. Dibenedetto & D. J. Diller, Some a-priori estimates for a singular evolution equation in thin film dynamics, preprint.

  8. M. B. Williams & S. H. Davis, Nonlinear theory of film rupture, Journal of Colloid and Interface Science 90 (1982), 220–228.

    Google Scholar 

  9. F. Bernis, Viscous flows, fourth order nonlinear degenerate parabolic equations and singular elliptic problems, to appear in Free Boundary Problems, 1993 Toledo, Diaz, Herrero, Linan & Vazquez, editors, Pitman Research Notes in Mathematics.

  10. A. L. Bertozzi, Loss and gain of regularity in a lubrification equation for thin viscous films, to appear in Free Boundary Problems, 1993 Toledo, Diaz, Herrero, Linan & Vazquez, editors, Pitman Research Notes in Mathematics.

  11. A. L. Bertozzi & M. Pugh, The lubrification approximation for thin viscous films: regularity and long time behavior of weak solutions, preprint.

  12. A. L. Bertozzi & M. Pugh, The lubrification approximation for thin viscous films: the moving contact line with a porous media cut off of the van der Waals interactions, preprint.

Download references

Author information

Authors and Affiliations

  1. Istituto per le Applicazioni del Calcolo “Mauro Picone”, Viale del Policlinico 137, 00161, Roma

    Elena Beretta, Michiel Bertsch & Roberta Dal Passo

  2. Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, 00133, Roma

    Elena Beretta, Michiel Bertsch & Roberta Dal Passo

Authors
  1. Elena Beretta
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michiel Bertsch
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Roberta Dal Passo
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by M. Gurtin

Rights and permissions

Reprints and permissions

About this article

Cite this article

Beretta, E., Bertsch, M. & Dal Passo, R. Nonnegative solutions of a fourth-order nonlinear degenerate parabolic equation. Arch. Rational Mech. Anal. 129, 175–200 (1995). https://doi.org/10.1007/BF00379920

Download citation

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00379920

Keywords

Search

Navigation