Sharp criteria for the waiting time phenomenon in solutions to the thin-film equation
De Nitti N, Fischer J (2022)
Publication Type: Journal article
Publication year: 2022
Journal
DOI: 10.1080/03605302.2022.2056702
Abstract
We establish sharp criteria for the instantaneous propagation of free boundaries in solutions to the thin-film equation. The criteria are formulated in terms of the initial distribution of mass (as opposed to previous almost-optimal results), reflecting the fact that mass is a locally conserved quantity for the thin-film equation. In the regime of weak slippage, our criteria are at the same time necessary and sufficient. The proof of our upper bounds on free boundary propagation is based on a strategy of "propagation of degeneracy" down to arbitrarily small spatial scales: We combine estimates on the local mass and estimates on energies to show that "degeneracy" on a certain space-time cylinder entails "degeneracy" on a spatially smaller space-time cylinder with the same time horizon. The derivation of our lower bounds on free boundary propagation is based on a combination of a monotone quantity and almost optimal estimates established previously by the second author with a new estimate connecting motion of mass to entropy production.
Authors with CRIS profile
Nicola De Nitti
Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)
Involved external institutions
Austria (AT)How to cite
APA:
De Nitti, N., & Fischer, J. (2022). Sharp criteria for the waiting time phenomenon in solutions to the thin-film equation. Communications in Partial Differential Equations. https://dx.doi.org/10.1080/03605302.2022.2056702
MLA:
De Nitti, Nicola, and Julian Fischer. "Sharp criteria for the waiting time phenomenon in solutions to the thin-film equation." Communications in Partial Differential Equations (2022).
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