Volume 25, 2019
|Number of page(s)||22|
|Published online||14 October 2019|
Gradient flow approach to an exponential thin film equation: global existence and latent singularity
Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay,
2 Department of Mathematics, Duke University, Durham, NC 27708, USA.
3 Department of Mathematics and Department of Physics, Duke University, Durham, NC 27708, USA.
4 Department of Mathematical Sciences, Lakehead University, Thunder Bay, ON P7B5E1, Canada.
5 Department of Mathematics and Statistics, McGill University, Montreal, QC H3A0B9, Canada.
* Corresponding author: email@example.com
Accepted: 12 June 2018
In this work, we study a fourth order exponential equation, ut = Δe−Δu derived from thin film growth on crystal surface in multiple space dimensions. We use the gradient flow method in metric space to characterize the latent singularity in global strong solution, which is intrinsic due to high degeneration. We define a suitable functional, which reveals where the singularity happens, and then prove the variational inequality solution under very weak assumptions for initial data. Moreover, the existence of global strong solution is established with regular initial data.
Mathematics Subject Classification: 35K65 / 35R06 / 49J40
Key words: Fourth-order exponential parabolic equation / Radon measure / global strong solution / latent singularity / curve of maximal slope
© EDP Sciences, SMAI 2019
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.