### The thin film equation with $2 \leq n<3$: finite speed of propagation in terms of the $L^1$-norm

#### Abstract

We consider the equation $u_t+(u^nu_{xxx})_x=0$ with $2\le n <3$ and establish an estimate for the finite speed of propagation of the support of compactly supported nonnegative solutions. The estimate depends only on the $L^1$-norm and is valid a posteriorifor strong solutions obtained through a Bernis-Friedman regularization.

#### Article information

Source
Adv. Differential Equations Volume 3, Number 5 (1998), 625-642.

Dates
First available in Project Euclid: 18 April 2013

Mathematical Reviews number (MathSciNet)
MR1665858

Zentralblatt MATH identifier
0953.35072

#### Citation

Hulshof, Josephus; Shishkov, Andrey E. The thin film equation with $2 \leq n&lt;3$: finite speed of propagation in terms of the $L^1$-norm. Adv. Differential Equations 3 (1998), no. 5, 625--642.https://projecteuclid.org/euclid.ade/1366292556