Abstract
We investigate the extinction behaviour of a fourth order degenerate diffusion equation in a bounded domain, the model representing the flow of a viscous fluid over edges at which zero contact angle conditions hold. The extinction time may be finite or infinite and we distinguish between the two cases by identification of appropriate similarity solutions. In certain cases, an unphysical mass increase may occur for early time and the solution may become negative; an appropriate remedy for this is noted. Numerical simulations supporting the analysis are included.
| Original language | English |
|---|---|
| Pages (from-to) | 135-157 |
| Number of pages | 23 |
| Journal | European Journal of Applied Mathematics |
| Volume | 12 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2001 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
Cite this
Asymptotic behaviour of the thin film equation in bounded domains. / Bowen, Mark; King, J. R.
In: European Journal of Applied Mathematics, Vol. 12, No. 2, 2001, p. 135-157.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Asymptotic behaviour of the thin film equation in bounded domains
AU - Bowen, Mark
AU - King, J. R.
PY - 2001
Y1 - 2001
N2 - We investigate the extinction behaviour of a fourth order degenerate diffusion equation in a bounded domain, the model representing the flow of a viscous fluid over edges at which zero contact angle conditions hold. The extinction time may be finite or infinite and we distinguish between the two cases by identification of appropriate similarity solutions. In certain cases, an unphysical mass increase may occur for early time and the solution may become negative; an appropriate remedy for this is noted. Numerical simulations supporting the analysis are included.
AB - We investigate the extinction behaviour of a fourth order degenerate diffusion equation in a bounded domain, the model representing the flow of a viscous fluid over edges at which zero contact angle conditions hold. The extinction time may be finite or infinite and we distinguish between the two cases by identification of appropriate similarity solutions. In certain cases, an unphysical mass increase may occur for early time and the solution may become negative; an appropriate remedy for this is noted. Numerical simulations supporting the analysis are included.
UR - http://www.scopus.com/inward/record.url?scp=0035595141&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0035595141&partnerID=8YFLogxK
U2 - 10.1017/S0956792501004417
DO - 10.1017/S0956792501004417
M3 - Article
AN - SCOPUS:0035595141
VL - 12
SP - 135
EP - 157
JO - European Journal of Applied Mathematics
JF - European Journal of Applied Mathematics
SN - 0956-7925
IS - 2
ER -