Osaka Journal of Mathematics

Large time behavior of solutions to the generalized Burgers equations

Masakazu Kato

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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

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

First available in Project Euclid: 7 January 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


Kato, Masakazu. Large time behavior of solutions to the generalized Burgers equations. Osaka J. Math. 44 (2007), no. 4, 923--943.

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