Uniqueness for the thin-film equation with a Dirac mass as initial data
Open Access
- 14 February 2018
- journal article
- research article
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 146 (6), 2623-2635
- https://doi.org/10.1090/proc/13935
Abstract
We show the uniqueness of strong solutions for the thin-film equation u(t) + (uu(xxx))(x) = 0 with initial data u(0) = m delta, m > 0, where delta is the Dirac mass at the origin. In particular, the solution is the source type one obtained by Smyth and Hill. The argument is based on an entropy estimate for the equation in self-similar variables.Keywords
Funding Information
- National Science Foundation (1716466, 1211806)
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