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UNIQUENESS FOR THE THIN-FILM EQUATION WITH A DIRAC MASS AS INITIAL DATA
Journal article   Open access  Peer reviewed

UNIQUENESS FOR THE THIN-FILM EQUATION WITH A DIRAC MASS AS INITIAL DATA

Mohamed Majdoub, Nader Masmoudi and Slim Tayachi
Proceedings of the American Mathematical Society, Vol.146(6), pp.2623-2635
01/06/2018
DOI: https://doi.org/10.1090/proc/13935

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
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.
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https://doi.org/10.1090/proc/13935View
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