## Advances in Differential Equations

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

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

Josephus Hulshof and Andrey E. Shishkov

#### 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
posteriori*for 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

**Permanent link to this document**

https://projecteuclid.org/euclid.ade/1366292556

**Mathematical Reviews number (MathSciNet)**

MR1665858

**Zentralblatt MATH identifier**

0953.35072

**Subjects**

Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]

Secondary: 76D99: None of the above, but in this section

#### Citation

Hulshof, Josephus; Shishkov, Andrey E. The thin film equation with $2 \leq n<3$: 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