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Graduate School of Science / Faculty of Science >
Hokkaido University Preprint Series in Mathematics >
ON A DIFFUSION EQUATION WITH RUPTURE
| Title: | ON A DIFFUSION EQUATION WITH RUPTURE |
| Authors: | Giga, Yoshikazu Browse this author →KAKEN DB | | Ueda, Yuki Browse this author |
| Issue Date: | 16-Oct-2023 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 1154 |
| Start Page: | 1 |
| End Page: | 18 |
| Abstract: | We propose a model to describe an evolution of a bubble cluster with rupture. In a special case, the equation is reduced to a single parabolic equation with evaporation for the thickness of a liquid layer covering bubbles. We postulate that a bubble collapses if this liquid layer becomes thin. We call this collapse a rupture. We prove for our model that there is a periodic-in-time solution if the place of rupture occurs only in the largest bubble. Numerical tests indicate that there may not exist a periodic solution if such an assumption is violated. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/90568 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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