## Differential and Integral Equations

### Long-time behavior in scalar conservation laws

#### Abstract

We consider the long-time behavior of the entropy solution of a first-order scalar conservation law on a Riemannian manifold. In the case of the torus, we show that, under a weak property of genuine non-linearity of the flux, the solution converges to its average value in $L^{p}$, $1\leq p < +\infty$. We give a partial result in the general case.

#### Article information

Source
Differential Integral Equations Volume 22, Number 3/4 (2009), 225-238.

Dates
First available in Project Euclid: 20 December 2012

https://projecteuclid.org/euclid.die/1356019771

Mathematical Reviews number (MathSciNet)
MR2492818

Zentralblatt MATH identifier
1240.35352

Subjects
Primary: 35L65: Conservation laws 35B40: Asymptotic behavior of solutions

#### Citation

Debussche, Arnaud; Vovelle, J. Long-time behavior in scalar conservation laws. Differential Integral Equations 22 (2009), no. 3/4, 225--238.https://projecteuclid.org/euclid.die/1356019771