表題番号：2018B-104
日付：2019/04/05

研究課題Drainage problems for the multidimensional thin film equation

研究者所属（当時） | 資格 | 氏名 | |
---|---|---|---|

（代表者） | 理工学術院 国際理工学センター（理工学術院） | 准教授 | ボーウェン マーク |

（連携研究者） | Duke University | Professor | T. P. Witelski |

（連携研究者） | Bucknell University | Professor | L. Smolka |

- 研究成果概要
- 1) Working with Professor T P Witelski (Duke University, USA), we have
been studying out-diffusion solutions of the so-called
thin film equation (a fourth order parabolic partial differential
equation) on a finite multi-dimensional domain; this extends our recent
previous work on the one-dimensional problem.

While considering this problem, we decided first to make a preliminary study of the related problem for the lower (second) order porous medium equation. In this context, we have constructed analytically self-similar solutions that act as large time attractors for solutions defined on sectorial [quarter, half-plane and three-quarter-plane] domains. We have confirmed these results using numerical simulations.

2) While working on this project, I established a new working relationship with Professor L. Smolka (Bucknell University, USA) looking at how thin films evolve in a periodic domain (corresponding physically to the external surface of a cylinder) under the combined effects of gravity (drainage) and thermal stresses (leading to a non-convex convective flux of fluid). The interaction of convective effects and surface tension (fourth order parabolic terms) yields solutions containing non-classical shock dynamics, such as undercompressive-compressive shock pairs and undercompressive shocks-rarefaction fans. We are currently writing up the results of this research for publication in the near future.