## Osaka Journal of Mathematics

- Osaka J. Math.
- Volume 44, Number 4 (2007), 923-943.

### Large time behavior of solutions to the generalized Burgers equations

#### Abstract

We study large time behavior of the solutions to the initial value problem for the generalized Burgers equation. It is known that the solution tends to a self-similar solution to the Burgers equation at the rate $t^{-1} \log t$ in $L^{\infty}$ as $t \to \infty$. The aim of this paper is to show that the rate is optimal under suitable assumptions and to obtain the second asymptotic profile of large time behavior of the solutions.

#### Article information

**Source**

Osaka J. Math., Volume 44, Number 4 (2007), 923-943.

**Dates**

First available in Project Euclid: 7 January 2008

**Permanent link to this document**

https://projecteuclid.org/euclid.ojm/1199719413

**Mathematical Reviews number (MathSciNet)**

MR2383818

**Zentralblatt MATH identifier**

1132.35311

**Subjects**

Primary: 35B40: Asymptotic behavior of solutions

Secondary: 35L65: Conservation laws

#### Citation

Kato, Masakazu. Large time behavior of solutions to the generalized Burgers equations. Osaka J. Math. 44 (2007), no. 4, 923--943. https://projecteuclid.org/euclid.ojm/1199719413