Uniqueness for the thin-film equation with a Dirac mass as initial data

Majdoub, Mohamed; Masmoudi, Nader; Tayachi, Slim

doi:10.1090/proc/13935

Uniqueness for the thin-film equation with a Dirac mass as initial data
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by Mohamed Majdoub, Nader Masmoudi and Slim Tayachi PDF

Proc. Amer. Math. Soc. 146 (2018), 2623-2635 Request permission

Abstract:

We show the uniqueness of strong solutions for the thin-film equation $u_t + (u u_{xxx})_x =0$ 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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