Details
| Original language | English |
|---|---|
| Pages (from-to) | 1656-1678 |
| Number of pages | 23 |
| Journal | SIAM Journal on Mathematical Analysis |
| Volume | 50 |
| Issue number | 2 |
| Early online date | 20 Mar 2018 |
| Publication status | Published - 2018 |
Abstract
In this paper the model for a highly viscous droplet sliding down an inclined plane is analyzed. It is shown that, provided the slope is not too steep, the corresponding moving boundary problem possesses classical solutions. Well-posedness is lost when the relevant linearization ceases to be parabolic. This occurs above a critical incline which depends on the shape of the initial wetted region as well as on the liquid's mass. It is also shown that translating circular solutions are asymptotically stable if the kinematic boundary condition is given by an affine function and provided the incline is small.
Keywords
- Contact angle motion, Moving boundary problem, Sliding droplet, Translating solutions
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: SIAM Journal on Mathematical Analysis, Vol. 50, No. 2, 2018, p. 1656-1678.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On a model for a sliding droplet: Well-posedness and stability of translating circular solutions
AU - Guidott, Patrick
AU - Walker, Christoph
PY - 2018
Y1 - 2018
N2 - In this paper the model for a highly viscous droplet sliding down an inclined plane is analyzed. It is shown that, provided the slope is not too steep, the corresponding moving boundary problem possesses classical solutions. Well-posedness is lost when the relevant linearization ceases to be parabolic. This occurs above a critical incline which depends on the shape of the initial wetted region as well as on the liquid's mass. It is also shown that translating circular solutions are asymptotically stable if the kinematic boundary condition is given by an affine function and provided the incline is small.
AB - In this paper the model for a highly viscous droplet sliding down an inclined plane is analyzed. It is shown that, provided the slope is not too steep, the corresponding moving boundary problem possesses classical solutions. Well-posedness is lost when the relevant linearization ceases to be parabolic. This occurs above a critical incline which depends on the shape of the initial wetted region as well as on the liquid's mass. It is also shown that translating circular solutions are asymptotically stable if the kinematic boundary condition is given by an affine function and provided the incline is small.
KW - Contact angle motion
KW - Moving boundary problem
KW - Sliding droplet
KW - Translating solutions
UR - http://www.scopus.com/inward/record.url?scp=85047317844&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1705.05492
DO - 10.48550/arXiv.1705.05492
M3 - Article
AN - SCOPUS:85047317844
VL - 50
SP - 1656
EP - 1678
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
SN - 0036-1410
IS - 2
ER -