---
OA_type: closed access
_id: '1317'
abstract:
- lang: eng
  text: We analyze the behaviour of free boundaries in thin-film flow in the regime
    of strong slippage n∈[1,2) and in the regime of very weak slippage n∈,3) qualitatively
    and quantitatively. In the regime of strong slippage, we construct initial data
    which are bounded from above by the steady state but for which nevertheless instantaneous
    forward motion of the free boundary occurs. This shows that the initial behaviour
    of the free boundary is not determined just by the growth of the initial data
    at the free boundary. Note that this is a new phenomenon for degenerate parabolic
    equations which is specific for higher-order equations. Furthermore, this result
    resolves a controversy in the literature over optimality of sufficient conditions
    for the occurrence of a waiting time phenomenon. In contrast, in the regime of
    very weak slippage we derive lower bounds on free boundary propagation which are
    optimal in the sense that they coincide up to a constant factor with the known
    upper bounds. In particular, in this regime the growth of the initial data at
    the free boundary fully determines the initial behaviour of the interface.
article_processing_charge: No
article_type: original
author:
- first_name: Julian L
  full_name: Fischer, Julian L
  id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
  last_name: Fischer
  orcid: 0000-0002-0479-558X
citation:
  ama: 'Fischer JL. Behaviour of free boundaries in thin-film flow: The regime of
    strong slippage and the regime of very weak slippage. <i>Annales de l’Institut
    Henri Poincare (C) Non Linear Analysis</i>. 2016;33(5):1301-1327. doi:<a href="https://doi.org/10.1016/j.anihpc.2015.05.001">10.1016/j.anihpc.2015.05.001</a>'
  apa: 'Fischer, J. L. (2016). Behaviour of free boundaries in thin-film flow: The
    regime of strong slippage and the regime of very weak slippage. <i>Annales de
    l’Institut Henri Poincare (C) Non Linear Analysis</i>. EMS Press. <a href="https://doi.org/10.1016/j.anihpc.2015.05.001">https://doi.org/10.1016/j.anihpc.2015.05.001</a>'
  chicago: 'Fischer, Julian L. “Behaviour of Free Boundaries in Thin-Film Flow: The
    Regime of Strong Slippage and the Regime of Very Weak Slippage.” <i>Annales de
    l’Institut Henri Poincare (C) Non Linear Analysis</i>. EMS Press, 2016. <a href="https://doi.org/10.1016/j.anihpc.2015.05.001">https://doi.org/10.1016/j.anihpc.2015.05.001</a>.'
  ieee: 'J. L. Fischer, “Behaviour of free boundaries in thin-film flow: The regime
    of strong slippage and the regime of very weak slippage,” <i>Annales de l’Institut
    Henri Poincare (C) Non Linear Analysis</i>, vol. 33, no. 5. EMS Press, pp. 1301–1327,
    2016.'
  ista: 'Fischer JL. 2016. Behaviour of free boundaries in thin-film flow: The regime
    of strong slippage and the regime of very weak slippage. Annales de l’Institut
    Henri Poincare (C) Non Linear Analysis. 33(5), 1301–1327.'
  mla: 'Fischer, Julian L. “Behaviour of Free Boundaries in Thin-Film Flow: The Regime
    of Strong Slippage and the Regime of Very Weak Slippage.” <i>Annales de l’Institut
    Henri Poincare (C) Non Linear Analysis</i>, vol. 33, no. 5, EMS Press, 2016, pp.
    1301–27, doi:<a href="https://doi.org/10.1016/j.anihpc.2015.05.001">10.1016/j.anihpc.2015.05.001</a>.'
  short: J.L. Fischer, Annales de l’Institut Henri Poincare (C) Non Linear Analysis
    33 (2016) 1301–1327.
date_created: 2018-12-11T11:51:20Z
date_published: 2016-10-01T00:00:00Z
date_updated: 2026-05-06T07:02:19Z
day: '01'
doi: 10.1016/j.anihpc.2015.05.001
extern: '1'
intvolume: '        33'
issue: '5'
keyword:
- Thin-film equation
- Free boundary
- Waiting time
- Qualitative behaviour
- Higher-order parabolic equation
- Degenerate parabolic equation
language:
- iso: eng
month: '10'
oa_version: None
page: 1301 - 1327
publication: Annales de l'Institut Henri Poincare (C) Non Linear Analysis
publication_identifier:
  eissn:
  - 1873-1430
  issnl:
  - 0294-1449
publication_status: published
publisher: EMS Press
publist_id: '5952'
quality_controlled: '1'
status: public
title: 'Behaviour of free boundaries in thin-film flow: The regime of strong slippage
  and the regime of very weak slippage'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 33
year: '2016'
...