表題番号：2022R-031
日付：2023/03/08
研究課題Cauchy‑Dirichlet Problems for the Porous Medium 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） | 教授 | ボーウェン マーク |
| （連携研究者） | University of Nottingham, UK | Professor | J. R. King |
| （連携研究者） | Duke University, USA | Professor | T. P. Witelski |
- 研究成果概要
- We used a combination of formal asymptotic methods supported by detailed numerical computations in order to investigate solutions to Cauchy-Dirichlet problems for the porous medium equation on a variety of two-dimensional domains. Such problems can arise physically from consideration of the spreading dynamics of a thin liquid film, where the boundary of the domain acts as an edge over which the film can drain.This research was undertaken as part of an international collaboration with Professor J. R. King (UK) and Professor T. P. Witelski (USA).This work has been published as:Cauchy-Dirichlet Problems for the Porous Medium Equation,M. Bowen, J. R. King and T. P. Witelski,Disc. Cont. Dyn. Sys., 2023, 43(3&4): 1143-1174. doi: 10.3934/dcds.2022182Special issue celebrating the 75th Birthday of Professor Juan Luis Vazquez.As an outcome of this work, we highlighted a number of open problems that deserve further rigorous analysis.