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

Mohamed Majdoub; Nader Masmoudi; Slim Tayachi

doi:10.1090/proc/13935

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

Mohamed Majdoub, Nader Masmoudi, Slim Tayachi

Research output: Contribution to journal › Article › peer-review

Abstract

We show the uniqueness of strong solutions for the thin-film equation u_t +(uu_xxx)_x = 0 with initial data u(0) = mδ, m > 0, where δ 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.

Original language	English (US)
Pages (from-to)	2623-2635
Number of pages	13
Journal	Proceedings of the American Mathematical Society
Volume	146
Issue number	6
DOIs	https://doi.org/10.1090/proc/13935
State	Published - 2018

Keywords

Entropy estimates
Self-similar variables
Thin-film equation
Uniqueness
Zero contact angle

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/proc/13935

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title = "Uniqueness for the thin-film equation with a dirac mass as initial data",

abstract = "We show the uniqueness of strong solutions for the thin-film equation ut +(uuxxx)x = 0 with initial data u(0) = mδ, m > 0, where δ 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 = "Entropy estimates, Self-similar variables, Thin-film equation, Uniqueness, Zero contact angle",

author = "Mohamed Majdoub and Nader Masmoudi and Slim Tayachi",

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AU - Majdoub, Mohamed

AU - Masmoudi, Nader

AU - Tayachi, Slim

PY - 2018

Y1 - 2018

N2 - We show the uniqueness of strong solutions for the thin-film equation ut +(uuxxx)x = 0 with initial data u(0) = mδ, m > 0, where δ 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.

AB - We show the uniqueness of strong solutions for the thin-film equation ut +(uuxxx)x = 0 with initial data u(0) = mδ, m > 0, where δ 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.

KW - Entropy estimates

KW - Self-similar variables

KW - Thin-film equation

KW - Uniqueness

KW - Zero contact angle

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

Abstract

Keywords

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