On one nonlinear mathematical model of blood circulation with the vessel walls reaction within the hereditary theory

Abstract

The research demonstrates sufficient conditions of the existence and uniqueness for the solution in the oscillation mathematical model of the blood flow under nonlinear dissipative forces action within the theory of he-reditary tube with biofactor. The obtained qualitative results advocate the application of Galerkin method to the above-mentioned problem. These re-sults facilitated the application of different (explicit and implicit) numerical methods in further studies of the dynamical characteristics of solutions in the considered oscillation mathematical models. Numerical integration of the movement equations by Runge-Kutta 4th order method and Geer 2nd or-der method in a model case within this research enabled the estimation of the influence of different physical and mechanical factors on the amplitude and frequency of the oscillation process. The use of hybrid methods for the oscillation modeling in the nonlinear isotropic elastic environment on the example of a vessel enabled the formulation of the equation of an object’s mechanical state based on energy approaches and the theory of mechanical fields in the continuous environments.