## Osaka Journal of Mathematics

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

Masakazu Kato

#### 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

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

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