@article{AIHPC_2004__21_2_255_0, author = {Gr\"un, G\"unther}, title = {Droplet spreading under weak slippage : the waiting time phenomenon}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {255--269}, publisher = {Elsevier}, volume = {21}, number = {2}, year = {2004}, doi = {10.1016/j.anihpc.2003.02.002}, mrnumber = {2047357}, zbl = {1062.35012}, language = {en}, url = {https://www.numdam.org/articles/10.1016/j.anihpc.2003.02.002/} }
TY - JOUR AU - Grün, Günther TI - Droplet spreading under weak slippage : the waiting time phenomenon JO - Annales de l'I.H.P. Analyse non linéaire PY - 2004 SP - 255 EP - 269 VL - 21 IS - 2 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.anihpc.2003.02.002/ DO - 10.1016/j.anihpc.2003.02.002 LA - en ID - AIHPC_2004__21_2_255_0 ER -
%0 Journal Article %A Grün, Günther %T Droplet spreading under weak slippage : the waiting time phenomenon %J Annales de l'I.H.P. Analyse non linéaire %D 2004 %P 255-269 %V 21 %N 2 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.anihpc.2003.02.002/ %R 10.1016/j.anihpc.2003.02.002 %G en %F AIHPC_2004__21_2_255_0
Grün, Günther. Droplet spreading under weak slippage : the waiting time phenomenon. Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004) no. 2, pp. 255-269. doi : 10.1016/j.anihpc.2003.02.002. https://www.numdam.org/articles/10.1016/j.anihpc.2003.02.002/
[1] Nonnegative solutions of a fourth order nonlinear degenerate parabolic equation, Arch. Rational Mech. Anal. 129 (1995) 175-200. | MR | Zbl
, , ,[2] Viscous flows, fourth order nonlinear degenerate parabolic equations and singular elliptic problems, in: , , , (Eds.), Free Boundary Problems: Theory and Applications, Pitman Research Notes in Mathematics, vol. 323, Longman, Harlow, 1995, pp. 40-56. | MR | Zbl
,[3] Finite speed of propagation and continuity of the interface for thin viscous flows, Adv. Differential Equations 1 (3) (1996) 337-368. | MR | Zbl
,[4] The thin viscous flow equation in higher space dimensions, Adv. Differential Equations 3 (1998) 417-440. | MR | Zbl
, , , ,[5] 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
, , ,[6] A waiting time phenomenon for thin film equations, Ann. Scuola Norm. Sup. Pisa 30 (2001) 437-463. | Numdam | MR | Zbl
, , ,[7] The thin film equation with nonlinear diffusion, Comm. Partial Differential Equations 26 (2001) 1509-1557. | MR | Zbl
, , ,[8] Wetting: statistics and dynamics, Rev. Modern Phys. 57 (1985) 827-863.
,[9] Source-type solutions to thin-film equations in higher space dimensions, European J. Appl. Math. 8 (1997) 507-524. | MR | Zbl
, ,[10] Droplet spreading under weak slippage: a basic result on finite speed of propagation, SIAM J. Math. Anal. 34 (2003) 992-1006. | MR | Zbl
,[11] On Bernis' interpolation inequalities in multiple space dimensions, Z. Anal. Anwendungen 20 (2001) 987-998. | MR | Zbl
,[12] On free boundary problems arising in thin film flow, Habilitation thesis, University of Bonn, 2001.
,[13] Droplet spreading under weak slippage: the optimal asymptotic propagation rate in the multi-dimensional case, Interfaces Free Bound. 4 (2002) 309-323. | MR | Zbl
,[14] Note on a theorem of Hilbert, Math. Z. 6 (1920) 314-317. | JFM | MR
,[15] Inequalities, Cambridge University Press, Cambridge, 1934. | JFM
, , ,[16] 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
, ,[17] On the roughness-induced effective boundary conditions for an incompressible viscous flow, J. Differential Equations 170 (2001) 96-122. | MR | Zbl
, ,[18] Hardy-Type Inequalities, Pitman Research Notes, vol. 219, Longman, Harlow, 1990. | MR | Zbl
, ,[19] Long-scale evolution of thin liquid films, Rev. Modern Phys. 69 (1997) 932-977.
, , ,[20] Lubrication approximation with prescribed non-zero contact angle: an existence result, Comm. Partial Differential Equations 23 (1998) 2077-2164. | MR | Zbl
,[21] Équations elliptiques du second ordre à coefficients discontinus, Les presses de l'université de Montréal, Montréal, 1966. | MR | Zbl
,- Well-posedness and blow-up of solutions for the p(l)-biharmonic wave equation with singular dissipation and variable-exponent logarithmic source, Journal of Pseudo-Differential Operators and Applications, Volume 16 (2025) no. 1 | DOI:10.1007/s11868-025-00680-z
- Global existence and blow‐up of solutions for a class of p
‐biharmonic wave equations with damping terms and power sources, Mathematical Methods in the Applied Sciences, Volume 48 (2025) no. 1, p. 218 | DOI:10.1002/mma.10324 - Asymptotic behaviors of global weak solutions for an epitaxial thin film growth equation, Nonlinear Analysis: Real World Applications, Volume 81 (2025), p. 104209 | DOI:10.1016/j.nonrwa.2024.104209
- On a singular epitaxial thin‐film growth equation involving logarithmic nonlinearity, Mathematical Methods in the Applied Sciences, Volume 47 (2024) no. 7, p. 5699 | DOI:10.1002/mma.9887
- Interface Propagation Properties for a Nonlocal Thin-Film Equation, SIAM Journal on Mathematical Analysis, Volume 56 (2024) no. 1, p. 173 | DOI:10.1137/22m1510297
- On a singular parabolic p-biharmonic equation with logarithmic nonlinearity, Nonlinear Analysis: Real World Applications, Volume 70 (2023), p. 103780 | DOI:10.1016/j.nonrwa.2022.103780
- Droplet motion with contact-line friction: long-time asymptotics in complete wetting, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Volume 479 (2023) no. 2274 | DOI:10.1098/rspa.2023.0090
- Sharp criteria for the waiting time phenomenon in solutions to the thin-film equation, Communications in Partial Differential Equations, Volume 47 (2022) no. 7, p. 1394 | DOI:10.1080/03605302.2022.2056702
- Mathematical Theory of Higher-Order Degenerate Evolution Models, 2019 | DOI:10.15407/akademperiodyka.382.230
- The Navier-slip thin-film equation for 3D fluid films: Existence and uniqueness, Journal of Differential Equations, Volume 265 (2018) no. 11, p. 5832 | DOI:10.1016/j.jde.2018.07.015
- Optimal waiting time bounds for some flux-saturated diffusion equations, Communications in Partial Differential Equations, Volume 42 (2017) no. 4, p. 556 | DOI:10.1080/03605302.2017.1294179
- The interface dynamics of a surfactant drop on a thin viscous film, European Journal of Applied Mathematics, Volume 28 (2017) no. 4, p. 656 | DOI:10.1017/s0956792516000474
- Continuous maximal regularity on singular manifolds and its applications, Evolution Equations and Control Theory, Volume 5 (2016) no. 2, p. 303 | DOI:10.3934/eect.2016006
- Finite Speed of Propagation and Waiting Time Phenomena for Degenerate Parabolic Equations with Linear Growth Lagrangian, SIAM Journal on Mathematical Analysis, Volume 47 (2015) no. 3, p. 2426 | DOI:10.1137/130945077
- Well-posedness for the Navier-slip thin-film equation in the case of complete wetting, Journal of Differential Equations, Volume 257 (2014) no. 1, p. 15 | DOI:10.1016/j.jde.2014.03.010
- A Free Boundary Problem of Fourth Order: Classical Solutions in Weighted Hölder Spaces, Communications in Partial Differential Equations, Volume 35 (2010) no. 11, p. 2059 | DOI:10.1080/03605302.2010.494262
- Smooth zero-contact-angle solutions to a thin-film equation around the steady state, Journal of Differential Equations, Volume 245 (2008) no. 6, p. 1454 | DOI:10.1016/j.jde.2008.06.005
- Small- and Waiting-Time Behavior of the Thin-Film Equation, SIAM Journal on Applied Mathematics, Volume 67 (2007) no. 6, p. 1776 | DOI:10.1137/060667682
- Droplet Spreading Under Weak Slippage—Existence for the Cauchy Problem, Communications in Partial Differential Equations, Volume 29 (2005) no. 11-12, p. 1697 | DOI:10.1081/pde-200040193
Cité par 19 documents. Sources : Crossref