Steady states and dynamics of a thin-film-type equation with non-conserved mass
| dc.contributor.author | Ji, Hangjie | |
| dc.contributor.author | Witelski, Thomas | |
| dc.date.accessioned | 2021-06-01T15:30:21Z | |
| dc.date.available | 2021-06-01T15:30:21Z | |
| dc.date.issued | 2020-12 | |
| dc.date.updated | 2021-06-01T15:30:18Z | |
| dc.description.abstract | <jats:p>We study the steady states and dynamics of a thin-film-type equation with non-conserved mass in one dimension. The evolution equation is a non-linear fourth-order degenerate parabolic partial differential equation (PDE) motivated by a model of volatile viscous fluid films allowing for condensation or evaporation. We show that by changing the sign of the non-conserved flux and breaking from a gradient flow structure, the problem can exhibit novel behaviours including having two distinct classes of co-existing steady-state solutions. Detailed analysis of the bifurcation structure for these steady states and their stability reveals several possibilities for the dynamics. For some parameter regimes, solutions can lead to finite-time rupture singularities. Interestingly, we also show that a finite-amplitude limit cycle can occur as a singular perturbation in the nearly conserved limit.</jats:p> | |
| dc.identifier.issn | 0956-7925 | |
| dc.identifier.issn | 1469-4425 | |
| dc.identifier.uri | ||
| dc.language | en | |
| dc.publisher | Cambridge University Press (CUP) | |
| dc.relation.ispartof | European Journal of Applied Mathematics | |
| dc.relation.isversionof | 10.1017/s0956792519000330 | |
| dc.subject | Thin-film equation | |
| dc.subject | modified Allen-Cahn/Cahn-Hilliard equation | |
| dc.subject | non-conserved model | |
| dc.subject | fourth-order parabolic partial differential equations | |
| dc.title | Steady states and dynamics of a thin-film-type equation with non-conserved mass | |
| dc.type | Journal article | |
| duke.contributor.orcid | Witelski, Thomas|0000-0003-0789-9859 | |
| pubs.begin-page | 968 | |
| pubs.end-page | 1001 | |
| pubs.issue | 6 | |
| pubs.organisational-group | Trinity College of Arts & Sciences | |
| pubs.organisational-group | Mathematics | |
| pubs.organisational-group | Pratt | |
| pubs.organisational-group | Duke | |
| pubs.organisational-group | Pratt School of Engineering | |
| pubs.publication-status | Published | |
| pubs.volume | 31 |
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