Asymptotic behavior toward nonlinear waves for radially symmetric solutions of the multi-dimensional Burgers equation

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:266

Article

Hashimoto, Itsuko^1,2  Matsumura, Akitaka³ 

[1] Osaka City Univ, Osaka, Osaka, Japan

[2] Kansai Univ, Suita, Osaka, Japan

[3] Osaka Univ, Suita, Osaka, Japan

关键词: Asymptotic behavior;    Burgers equation;    Radially symmetric solution;   

DOI  :  10.1016/j.jde.2018.08.045

来源: Elsevier

【 摘 要 】

The present paper is concerned with the asymptotic behaviors of radially symmetric solutions for the multi-dimensional Burgers equation on the exterior domain in R-n, n >= 3, where the boundary and far field conditions are prescribed. We show that in some case where the corresponding 1-D Riemann problem for the non-viscous part admits a shock wave, the solution tends toward a linear superposition of stationary and rarefaction waves as time goes to infinity, and also show the decay rate estimates. Furthermore, we improve the results on the asymptotic stability of the stationary waves which are treated in the previous papers [2], [3]. Finally, for the case of n = 3, we give the complete classification of the asymptotic behaviors, which includes even a linear superposition of stationary and viscous shock waves. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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