Name
Abstract | ||
|---|---|---|
We consider a third order nonautonomous ODE that arises as a model of fluid accumulation in a two-dimensional thin-film flow driven by surface tension and gravity. With the appropriate matching conditions, the equation describes the inner structure of solutions around a stagnation point. In this paper we prove the existence of solutions that satisfy this problem. In order to prove the result we first transform the equation into a four-dimensional dynamical system. In this setting the problem consists of finding heteroclinic connections that are the intersection of a two-dimensional center-stable manifold and a three-dimensional center-unstable one. We then use a shooting argument that takes advantage of the information of the flow in the far-field; part of the analysis also requires the understanding of oscillatory solutions with large amplitude. The far-field is represented by invariant three-dimensional subspaces, and the flow on them needs to be understood; most of the necessary results in this regard were obtained in our previous work [SIAM J. Math. Anal., 44 (2012), pp. 1588-1616]. The analysis in that paper focuses on the understanding of oscillatory solutions, and some results are used in the current proof, although the structure of oscillations here is somewhat more complicated. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1137/120898930 | SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS |
Keywords | Field | DocType |
thin-film flow,stagnation point,oscillations | Mathematical analysis,Flow (psychology),Third order,Linear subspace,Stagnation point,Invariant (mathematics),Mathematics,Dynamical system,Manifold,Ode | Journal |
Volume | Issue | ISSN |
13 | 1 | 1536-0040 |
Citations | PageRank | References |
0 | 0.34 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| C. M. Cuesta | 1 | 4 | 3.38 |
| J. J. L. Velázquez | 2 | 13 | 8.41 |