On Riemann solutions under different initial periodic perturbations at two infinities for 1-d scalar convex conservation laws

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:268

Article

Yuan, Qian¹  Yuan, Yuan^2,3 

[1] Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China

[2] South China Normal Univ, South China Res Ctr Appl Math & Interdisciplinary, Guangzhou, Guangdong, Peoples R China

[3] Univ Brescia, Sez Matemat, DICATAM, Via Valotti 9, I-25133 Brescia, Italy

关键词: Conservation laws;    Shock waves;    Rarefaction waves;    Periodic perturbations;   

DOI  :  10.1016/j.jde.2019.11.008

来源: Elsevier

【 摘 要 】

This paper is concerned with the large time behaviors of the entropy solutions to one-dimensional scalar convex conservation laws, of which the initial data are assumed to approach two arbitrary L-infinity periodic functions as x -> -infinity and x ->+infinity, respectively. We show that the solutions approach the Riemann solutions at algebraic rates as time increases. Moreover, a new discovery in this paper is that the difference between the two periodic perturbations at two infinities may generate a constant shift on the background shock wave, which is different from the result in [11], where the two periodic perturbations are the same. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free