Asymptotic stability of rarefaction wave for a blood flow model

作者：Wei, Jing; Yao, Huancheng; Zhu, Changjiang^*

来源：MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2023, 46(8): 8680-8694.

DOI：10.1002/mma.9010

• asymptotic stability
• blood flow model
• Cauchy problem
• rarefaction wave

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 regarding 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 regarding nonlinear stability of some nontrivial profiles (i.e., non-constant function patterns) for the blood flow model.

• 单位
  华南农业大学