Finite speed of propagation for the thin-film equation in the spherical geometry
UDC 517.953 We show that a double degenerate thin-film equation obtained in modeling of a flow of viscous coating on the spherical surface has a finite speed of propagation for nonnegative strong solutions and, hence, there exists an interface or a free boundary separating the regions, where the s...
Збережено в:
| Дата: | 2019 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2019
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/1479 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | UDC 517.953
We show that a double degenerate thin-film equation obtained in modeling of a flow of viscous coating on the spherical surface has a finite speed of propagation for nonnegative strong solutions and, hence, there exists an interface or a free boundary separating the regions, where the solution $u>0$ and $u=0.$
Using local entropy estimates, we also obtain the upper bound for the rate of the interface propagation. |
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