Name
Abstract | ||
|---|---|---|
We study self-similar solutions of the thin-film equation h(t)+(h(m)h(xxx))(x) = 0 in {(x, t) : h(x, t) > 0} with m E (0, 4] that describe the lifting of an isolated touch-down point given by an initial profile of the form h(in) (x) = This provides a mechanism for nonuniqueness of the thin-film equation with m is an element of (2,4) since solutions with a persistent touch-down point also exist in this case. In order to prove the existence of the self-similar solutions, we need to study a four-dimensional continuous dynamical system. The proof consists of a shooting argument based on the identification of invariant regions and on suitable energy formulas. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1137/17M1141485 | SIAM JOURNAL ON MATHEMATICAL ANALYSIS |
Keywords | Field | DocType |
self-similar solutions,thin-film equation,nonuniqueness | Mathematical analysis,Pure mathematics,Thin-film equation,Invariant (mathematics),Dynamical system,Mathematics | Journal |
Volume | Issue | ISSN |
50 | 2 | 0036-1410 |
Citations | PageRank | References |
0 | 0.34 | 1 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| C. M. Cuesta | 1 | 4 | 3.38 |
| Hans Knüpfer | 2 | 0 | 1.69 |
| J. J. L. Velázquez | 3 | 13 | 8.41 |