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July 2016 Behavior of solutions for radially symmetric solutions for Burgers equation with a boundary corresponding to the rarefaction wave
Itsuko Hashimoto
Osaka J. Math. 53(3): 799-811 (July 2016).

Abstract

We investigate the large-time behavior of the radially symmetric solution for Burgers equation on the exterior of a small ball in multi-dimensional space, where the boundary data and the data at the far field are prescribed. In a previous paper [1], we showed that, for the case in which the boundary data is equal to $0$ or negative, the asymptotic stability is the same as that for the viscous conservation law. In the present paper, it is proved that if the boundary data is positive, the asymptotic state is a superposition of the stationary wave and the rarefaction wave, which is a new wave phenomenon. The proof is given using a standard $L^{2}$ energy method and the characteristic curve method.

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Itsuko Hashimoto. "Behavior of solutions for radially symmetric solutions for Burgers equation with a boundary corresponding to the rarefaction wave." Osaka J. Math. 53 (3) 799 - 811, July 2016.

Information

Published: July 2016
First available in Project Euclid: 5 August 2016

zbMATH: 1350.35030
MathSciNet: MR3533470

Subjects:
Primary: 35L60
Secondary: 37K40

Rights: Copyright © 2016 Osaka University and Osaka City University, Departments of Mathematics

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Vol.53 • No. 3 • July 2016
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