Asymptotic stability of rarefaction wave for a blood flow model
• Jing Wei,
• Huancheng Yao,
• Changjiang Zhu
Jing Wei
South China University of Technology School of Mathematics

Corresponding Author:majwei@mail.scut.edu.cn

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Huancheng Yao
College of Mathematics and Informatics, South China Agricultural University
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Changjiang Zhu
South China University of Technology
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## Abstract

This paper is concerned with nonlinear stability of rarefaction wave to the Cauchy problem for a blood flow model, which describes the motion of blood through axi-symmetric compliant vessels. Inspired by the stability analysis of classical $p$-system, we show the solution of this typical model tends time-asymptotically toward the rarefaction wave under some suitably small conditions and there are more difficulties in the proof due to the appearance of strong nonlinear terms including second-order derivative of $v$ with respect to the spatial variable $x$. The main result is proved by employing the elementary $L^2$ energy methods. This is the first result about nonlinear stability of some nontrivial profiles (i.e., non-constant function patterns) for the blood flow model.
16 Jul 2022Submitted to Mathematical Methods in the Applied Sciences
18 Jul 2022Assigned to Editor
18 Jul 2022Submission Checks Completed
22 Jul 2022Reviewer(s) Assigned
12 Dec 2022Review(s) Completed, Editorial Evaluation Pending
13 Dec 2022Editorial Decision: Accept