---
_id: '9335'
abstract:
- lang: eng
text: 'Various degenerate diffusion equations exhibit a waiting time phenomenon:
depending on the “flatness” of the compactly supported initial datum at the boundary
of the support, the support of the solution may not expand for a certain amount
of time. We show that this phenomenon is captured by particular Lagrangian discretizations
of the porous medium and the thin film equations, and we obtain sufficient criteria
for the occurrence of waiting times that are consistent with the known ones for
the original PDEs. For the spatially discrete solution, the waiting time phenomenon
refers to a deviation of the edge of support from its original position by a quantity
comparable to the mesh width, over a mesh-independent time interval. Our proof
is based on estimates on the fluid velocity in Lagrangian coordinates. Combining
weighted entropy estimates with an iteration technique à la Stampacchia leads
to upper bounds on free boundary propagation. Numerical simulations show that
the phenomenon is already clearly visible for relatively coarse discretizations.'
acknowledgement: This research was supported by the DFG Collaborative Research Center
TRR 109, “Discretization in Geometry and Dynamics”.
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
- first_name: Daniel
full_name: Matthes, Daniel
last_name: Matthes
citation:
ama: Fischer JL, Matthes D. The waiting time phenomenon in spatially discretized
porous medium and thin film equations. SIAM Journal on Numerical Analysis.
2021;59(1):60-87. doi:10.1137/19M1300017
apa: Fischer, J. L., & Matthes, D. (2021). The waiting time phenomenon in spatially
discretized porous medium and thin film equations. SIAM Journal on Numerical
Analysis. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/19M1300017
chicago: Fischer, Julian L, and Daniel Matthes. “The Waiting Time Phenomenon in
Spatially Discretized Porous Medium and Thin Film Equations.” SIAM Journal
on Numerical Analysis. Society for Industrial and Applied Mathematics, 2021.
https://doi.org/10.1137/19M1300017.
ieee: J. L. Fischer and D. Matthes, “The waiting time phenomenon in spatially discretized
porous medium and thin film equations,” SIAM Journal on Numerical Analysis,
vol. 59, no. 1. Society for Industrial and Applied Mathematics, pp. 60–87, 2021.
ista: Fischer JL, Matthes D. 2021. The waiting time phenomenon in spatially discretized
porous medium and thin film equations. SIAM Journal on Numerical Analysis. 59(1),
60–87.
mla: Fischer, Julian L., and Daniel Matthes. “The Waiting Time Phenomenon in Spatially
Discretized Porous Medium and Thin Film Equations.” SIAM Journal on Numerical
Analysis, vol. 59, no. 1, Society for Industrial and Applied Mathematics,
2021, pp. 60–87, doi:10.1137/19M1300017.
short: J.L. Fischer, D. Matthes, SIAM Journal on Numerical Analysis 59 (2021) 60–87.
date_created: 2021-04-18T22:01:42Z
date_published: 2021-01-01T00:00:00Z
date_updated: 2023-08-08T13:10:40Z
day: '01'
department:
- _id: JuFi
doi: 10.1137/19M1300017
external_id:
arxiv:
- '1911.04185'
isi:
- '000625044600003'
intvolume: ' 59'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1911.04185
month: '01'
oa: 1
oa_version: Preprint
page: 60-87
publication: SIAM Journal on Numerical Analysis
publication_identifier:
issn:
- 0036-1429
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: The waiting time phenomenon in spatially discretized porous medium and thin
film equations
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 59
year: '2021'
...