Asymptotic stability of rarefaction wave for a blood flow model

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.