Existence Of Particle Solutions For Multi-layer Fluid-structure Coupling Under The Influence Of Nonlinear And Thermal Effect

In recent years,cardiovascular disease has seriously threatened the life and health of the people in our country,has become a major public health problem,prevention and treatment of cardiovascular disease is urgent.Cardiovascular disease modeling is one of the hottest areas of research,this paper deeply discusses the multi-layer nonlinear fluid-structure interaction problem and the existence of the solution under the condition of slip boundary and thermal effect,which has very important theoretical significance and application value for the study of cardiovascular disease.This work mainly includes the following aspects.1.Combined with the arterial structure,we established a more practical mathematical model of multi-layer arterial wall and blood interaction.The multi-layer structure consists of two layers:a thin nonlinear elastic layer that is in direct contact with the free fluid flow and a thick linear elastic layer that sits on top of the thin layer.By using operator splitting and time semi-discretization,the system is divided into two subproblems:fluid sub-problem and structural sub-problem.For the fluid sub-problem,we apply Lax-Milgram lemma to obtain the existence and uniqueness of the approximate solution of the fluid sub-problem,in particular,for the nonlinear structure sub-problem,we obtain the existence and uniqueness of the approximate solution by using Schaefer’s fixed point theorem and doing the cross product of the space.For weak convergence and weak*convergence,we prove this result by establishing a priori estimates,and then combine Simon’s theorem to prove strong convergence,and finally take the limit to obtain the existence of weak solutions.2.Combined with a more realistic picture of blood vascular dynamics,there is a horizontal velocity difference between the blood flow velocity and the displacement velocity of the vascular wall.Considering the effect of Cattaneo thermal effect on arteriosclerosis,a mathematical model of multi-layer blood vessels interaction with Navier slip boundary and thermal effect is proposed.Through the time discretization of operator splitting,the existence and uniqueness of the approximate solutions of the two subproblems are obtained respectively.We find that the heating terms v and q will cancel in the process of processing,and it is easy to prove the continuity of operator B.Then we get the prior estimates of the approximate solutions and derive the weak convergence and weak*convergence from the prior estimates.In particular,due to the slip boundary condition,a new compactness parameter is proposed to control the tangential velocity components at the interface,and the strong convergence results are obtained by Simon’s theorem.Finally we obtain the existence of weak solutions by taking the limit.This paper systematically analyzes the nonlinear multi-layer fluid-structure coupling problem and the existence of solutions under the influence of slip boundary and thermal effect,which can further promote the application of fluid-structure interaction problem in medicine.