Finite speed of propagation and continuity of the interface for thin viscous flows

Advances in Differential Equations

Volumn 1, Issue 3, 1996, Pages 337-368

  Bernis, Francisco ^a  

^a UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000254565     PISSN: 10799389     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (22)

1. E. Beretta, M. Bertsch and R. Dal Passo, Nonnegative solutions of a fourth order nonlinear degenerate parabolic equation, Arch. Rational Mech. Anal. 129 (1995), 175-200.
2. F. Bernis, Qualitative properties for some nonlinear higher order degenerate parabolic equations, Houston J. Math. 14 (1988),319-352.
3. F. Bernis, Viscous flows, fourth order nonlinear degenerate parabolic equations and singular elliptic problems, Free boundary problems: theory and applications (J. I. Diaz, M. A. Herrero, A. Liñan and J. L. Vazquez, eds.), Pitman Research Notes in Mathematics 323, Longman, Harlow, 1995, pp. 40-56.
4. F. Bernis and A. Friedman, Higher order nonlinear degenerate parabolic equations, J. Differential Equations 83 (1990), 179-206.
5. F. Bernis, L. A. Peletier and S. M. Williams, Source type solutions of a fourth order nonlinear degenerate parabolic equation, Nonlinear Anal. 18 (1992), 217-234.
6. A. L. Bertozzi, Loss and gain of regularity in a lubrication equation for thin viscous films, Free boundary problems: theory and applications (J. I. Diaz, M. A. Herrero, A. Liñan and J. L. Vazquez, eds.), Pitman Research Notes in Mathematics 323, Longman, Harlow, 1995, pp. 72-85.
7. A. L. Bertozzi, Symmetric singularity formation in lubrication-type equations for interface motion, SIAM J. Applied Math. (to appear).
8. A. L. Bertozzi, M. P. Brenner, T. F. Dupont and L. P. Kadanoff, Singularities and similarities in interface flows, Trends and Perspectives in Applied Mathematics (L. Sirovich, ed.), Vol. 100 of Applied Mathematical Sciences, Springer-Verlag, Berlin, 1994, pp. 155-208.
9. A. L. Bertozzi and M. Pugh, The lubrication approximation for thin viscous films: regularity and long time behavior of weak solutions, Comm. Pure Appl. Math. (to appear).
10. A. L. Bertozzi and M. Pugh, The lubrication approximation for thin viscous films: the moving contact line with a "porous media" cut offof the van der Waals interactions, Nonlinearity 7 (1994), 1535-1564.
11. S. Boatto, L. P. Kadanoffand P. Olla, Traveling-wave solutions to thin-film equations, Phys. Rev. E 48 (1993), 4423-4431.
12. P. Constantin, T. F. Dupont, R. E. Goldstein, L. P. Kadanoff, M. J. Shelley and Su-Min Zhou, Droplet breakup in a model of the Hele-Shaw cell, Phys. Rev. E 47 (1993), 4169-4181.
13. T. F. Dupont, R. E. Goldstein, L. P. Kadanoffand Su-Min Zhou, Finite-time singularity formation in Hele-Shaw systems, Phys. Rev. E 47 (1993), 4182-4196.
14. C. M. Elliott and H. Garcke, On the Cahn-Hilliard equation with degenerate mobility, SIAM J. Math. Anal. (to appear).
15. L. Giacomelli, Preprint, Università di Firenze (1995).
16. G. Grün, Degenerate parabolic differential equations of fourth order and a plasticity model with nonlocal hardening, Z. Anal. Anwendungen (to appear).
17. R. E. Goldstein, A. I. Pesci and M. J. Shelley, Topology transitions and singularities in viscous flows, Physical Rev. Letters 70 (1993), 3043-3046.
18. J. L. Lions and E. Magenes, "Probl̀emes aux limites non homogènes et applications," Vol. 1, Dunod, Paris, 1968.
19. L. Nirenberg, On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa 13 (1959),115-162.
20. L. Nirenberg, An extended interpolation inequality, Ann. Scuola Norm. Sup. Pisa 20 (1966),733-737.
21. N. F. Smyth and J. M. Hill, High-order nonlinear diffusion, IMA J. Appl. Math. 40 (1988), 73-86.
22. Yin Jingxue, On the existence of nonnegative continuous solutions of the Cahn-Hilliard equation, J. Differential Equations 97 (1992),310-327.