A waiting time phenomenon for thin film equations
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 30 (2001) no. 2, pp. 437-463.
@article{ASNSP_2001_4_30_2_437_0,
     author = {Dal Passo, Roberta and Giacomelli, Lorenzo and Gr\"un, G\"unther},
     title = {A waiting time phenomenon for thin film equations},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {437--463},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 30},
     number = {2},
     year = {2001},
     mrnumber = {1895718},
     zbl = {1024.35051},
     language = {en},
     url = {http://archive.numdam.org/item/ASNSP_2001_4_30_2_437_0/}
}
TY  - JOUR
AU  - Dal Passo, Roberta
AU  - Giacomelli, Lorenzo
AU  - Grün, Günther
TI  - A waiting time phenomenon for thin film equations
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 2001
SP  - 437
EP  - 463
VL  - 30
IS  - 2
PB  - Scuola normale superiore
UR  - http://archive.numdam.org/item/ASNSP_2001_4_30_2_437_0/
LA  - en
ID  - ASNSP_2001_4_30_2_437_0
ER  - 
%0 Journal Article
%A Dal Passo, Roberta
%A Giacomelli, Lorenzo
%A Grün, Günther
%T A waiting time phenomenon for thin film equations
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 2001
%P 437-463
%V 30
%N 2
%I Scuola normale superiore
%U http://archive.numdam.org/item/ASNSP_2001_4_30_2_437_0/
%G en
%F ASNSP_2001_4_30_2_437_0
Dal Passo, Roberta; Giacomelli, Lorenzo; Grün, Günther. A waiting time phenomenon for thin film equations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 30 (2001) no. 2, pp. 437-463. http://archive.numdam.org/item/ASNSP_2001_4_30_2_437_0/

[ 1 ] N.D. Alikakos, On the pointwise behavior of the solutions of the porous medium equation as t approaches zero or infinity, Nonlinear Anal. 9 (1985), 1095-1113. | MR | Zbl

[2] D.G. Aronson, "The porous medium equation", In A. Dold and B. Eckmann, editors, Nonlinear Diffusion Problems. Lecture Notes in Mathematics, 1224, Springer-Verlag, 1985. | MR | Zbl

[3] E. Beretta - M. Bertsch - R. Dal Passo, Nonnegative solutions of a fourth order nonlinear degenerate parabolic equation, Arch. Rat. Mech. Anal. 129 (1995), 175-200. | MR | Zbl

[4] 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 - J. L. Vazquez (eds.), Pitman Research Notes in Mathematics 323, Longman, Harlow, 1995, pp. 40-56. | MR | Zbl

[5] F. Bernis, Finite speed ofpropagation and continuity of the interfacefor thin viscous flows, Adv. Differential Equations 1 no. 3 (1996), 337-368. | MR | Zbl

[6] F. Bernis, Finite speed of propagation for thin viscous flows when 2 ≤ n < 3, C.R. Acad. Sci. Paris Sér. I Math. 322 (1996). | Zbl

[7] F. Bernis - A. Friedman, Higher order nonlinear degenerate parabolic equations, J. Differential Equations 83 (1990), 179-206. | MR | Zbl

[8] F. Bernis - L.A. Peletier - S.M. Williams, Source-type solutions of a fourth order nonlinear degenerate parabolic equations, Nonlinear Anal. 18 (1992), 217-234. | MR | Zbl

[9] A. Bertozzi - M. Pugh, The lubrication approximation for thin viscous films: the moving contact line with a porous media cut off of van der waals interactions, Nonlinearity 7 (1994), 1535-1564. | MR | Zbl

[10] A.L. Bertozzi - M. Pugh, The lubrication approximation for thin viscous films: regularity and long time behaviour of weak solutions, Nonlinear Anal. 18 (1992), 217-234.

[11] M. Bertsch - R. Dal Passo - H. Garcke - G. Grün, The thin viscous flow equation in higher space dimensions, Adv. Differential Equations 3 (1998), 417-440. | MR | Zbl

[12] R. Dal Passo - H. Garcke, Solutions of a fourth order degenerate parabolic equation with weak initial trace, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 28 (1999), 153-181. | Numdam | MR | Zbl

[13] R. Dal Passo - H. Garcke - G. Grün, On a fourth order degenerate parabolic equation: global entropy estimates and qualitative behaviour of solutions, SIAM J. Math. Anal. 29 (1998), 321-342. | MR | Zbl

[14] R. Dal Passo - L. Giacomelli - A. Shishkov, The thin film equation with nonlinear diffusion, Preprint Me.Mo.Mat. Department 2/2000, to appear in Comm. Partial Differential Equations. | MR | Zbl

[15] E.B. Dussan - S. Davis, On the motion of a fluid-fluid interface along a solid surface, J. Fluid Mech. 65 (1974), 71-95. | Zbl

[16] R. Ferreira - F. Bernis, Source-type solutions to thin-film equations in higher space dimensions, European J. Appl. Math. 8 (1997), 507-524. | MR | Zbl

[17] E. Gagliardo, Ulteriori properità di alcune classi di funzioni in piú variabili, Ricerche di Mat. (1959), 24-51. | MR | Zbl

[18] G. Grün, Degenerate parabolic equations of fourth order and a plasticity model with nonlocal hardening, Z. Anal. Anwendungen 14 (1995), 541-573. | MR | Zbl

[19] G. Grün - M. Rumpf, Nonnegativity preserving convergent schemes for the thin film equation, Numer. Mathematik 87 (2000), 113-152. | MR | Zbl

[20] G. Grün - M. Rumpf, Entropy consistent finite volume schemes for the thin film equation, In: "Finite volume schemes for complex applications II", R. Vilsmeier - F. Benkhaldoun - D. Hänel (eds.), Hermes Science Publications, Paris, 1999, pp. 205-214. | MR | Zbl

[21] J. Hulshof - A. Shishkov, The thin film equation with 2 ≤ n < 3: finite speed of propagation in terms of the l1-norm, Adv. Differential Equations 3 (1998), 625-642. | Zbl

[22] B.F. Knerr, The porous medium equation in one dimension, Trans. Amer. Math. Soc. 234 (1977), 381-415. | MR | Zbl

[23] L. Nirenberg, On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa, Cl. Sci. 13 (1959), 115-162. | EuDML | Numdam | MR | Zbl

[24] A. Oron - S.H. Davis - S.G. Bankoff, Long-scale evolution of thin liquid films, Reviews of Modem Physics 69 (1997), 932-977.

[25] F. Otto, Lubrication approximation with prescribed non-zero contact angle: an existence result, Comm. Partial Differential Equations 23 (1998), 2077-2164. | MR | Zbl

[26] N.F. Smyth - J.M. Hill, Higher order nonlinear diffusion, IMA J. Applied Mathematics 40 (1988), 73-86. | MR | Zbl

[27] G. Stampacchia, "Équations elliptiques du second ordre à coefficients discontinus", Les presses de l'université de Montréal, Montréal, 1966. | MR | Zbl

[28] J.L. Vazquez, An introduction to the mathematical theory of the porous medium equation, In: "Shape Optimization and Free Boundaries", M. C. Delfour-G. Sabidussi (eds.), Kluwer Academic Publishers, Netherlands, 1992, pp. 347-389. | MR | Zbl