Some Exact Solutions to the Problem of a Liquid Flow in a Contracting Elastic Vessel

Abstract

In this paper, we consider some exact solutions of the hemodynamic equations in a contracting vessel in a quasi-one-dimensional approximation in relation to the problems arising in the description of the lymph flow. Solutions for the linearized problem in the case of forced small contractions of the vessel’s lumen are given. An analytical solution of a nonlinear system is obtained and studied at the dependence of the vessel’s cross section only on time. Exact solutions are reproduced in the numerical calculation.