The thin viscous flow equation in higher space dimensions

Advances in Differential Equations

Volumn 3, Issue 3, 1998, Pages 417-440

  Bertsch, Michiel ^a   Passo, Roberta Dal ^a   Garcke, Harald ^b   Grün, Günther ^b  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

^b UNIVERSITY OF BONN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84894616360     PISSN: 10799389     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (21)

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, Viscous flows, fourth order nonlinear degenerate parabolic equations and singular elliptic problems, in: Free boundary problems: theory and applications (J.I. Diaz, M.A. Herrero, A. Linan and J.L. Vazquez, eds.), Pitman Research Notes in Mathematics 323, Longman, Harlow, 1995, 40-56.
3. F. Bernis, Finite speed of propagation and continuity of the interface for thin viscous flows, Adv. in Diff. Equations, 1(3) (1996), 337-368.
4. F. Bernis, Finite speed of propagation for thin viscous flows when 2 ≤ n < 3, C.R. Acad. Sci. Paris, Sér.I Math. 322 (1996), 1169-1174.
5. F. Bernis and A. Friedman, Higher order nonlinear degenerate parabolic equations, J. Diff. Equ., 83 (1990), 179-206.
6. F. Bernis, L.A. Peletier, and S.M. Williams, Source type solutions of a fourth order nonlinear degenerate parabolic equation, Nonlin. Anal., 18 (1992), 217-234.
7. A.L. Bertozzi and M. Pugh, The lubrication approximation for thin viscous films: regularity and long time behaviour of weak solutions, Comm. Pure Appl. Math., XLIX, No. 2 (1996), 85-123.
8. J.W. Cahn, C.M. Elliott, and A. Novick-Cohen, The Cahn-Hilliard equation with a concentration dependent mobility: Motion by minus the Laplacian of the mean curvature, European J. Appl. Math., 7(3) (1996), 287-301.
9. R. Dal Passo, H. Garcke, and G. Grün, On a fourth order degenerate parabolic equation: global entropy estimates and qualitative behaviour of solutions, to appear in SIAM J. Math. Anal., 29(2) (1998).
10. C.M. Elliott and H. Garcke, On the Cahn-Hilliard equation with degenerate mobility, SIAM J. Math. Anal., 27(2) (1996), 404-423.
11. C.M. Elliott and H. Garcke, Diffusional phase transition in multicomponent systems with a concentration dependent mobility matrix, Physica D, 109 (1997), 242-256.
12. R. Ferreira and F. Bernis, Source-type solutions to thin-film equations in higher dimensions, Euro. J. of Applied Mathematics, 8 (1997), 507-524.
13. E. Gagliardo, Ulteriori properietà di alcune classi di funzioni in piu variabli, Ricerche di Mat. Napoli, (1959), 24-51.
14. G. Grün, Degenerate parabolic differential equations of fourth order and a plasticity model with nonlocal hardening, Z. Anal. Anwendungen, 14 (1995), 541-574.
15. H.P. Greenspan, On the motion of a small viscous droplet that wets a surface, J. Fluid Mech., 84 (1978), 125-143.
16. R. Kersner and A. Shiskov, Existence of free-boundaries in thin-film theory, preprint.
17. J.L. Lions and E. Magenes, "Non-Homogeneous Boundary Value Problems and Applications I," Springer-Verlag, Berlin, 1972.
18. L. Nirenberg, On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa, 13 (1959), 115-162.
19. L. Nirenberg, An extended interpolation inequality, Ann. Scuola Norm. Sup. Pisa, 20 (1966), 733-737.
20. F. Otto, Lubrication approximation with prescribed non-zero contact angle: an existence result, SFB256 preprint no. 478, University Bonn.
21. p(0, T;B), Annali di Matematica Pura ed Applicata, 146 (1987), 65-96.