一个双曲-椭圆耦合系统解的存在唯一性
THE EXISTENCE AND UNIQUENESS OF THE SOLUTIONS TO THE HYPERBOLIC-ELLIPTIC COUPLED SYSTEM

本文研究了一个双曲-椭圆耦合系统.通过能量方法建立了有关微分算子的一些先验估计，构造了一个闭线性算子，证明了该闭线性算子为一个有界收缩线性算子半群的无穷小生成元.在此基础上，利用半群理论具体证明了双曲-椭圆耦合系统解的存在唯一性.
In this paper, we study the hyperbolic-elliptic coupled system. By the energy method, we establish a priori estimates of the differential operator, construct the closed linear operator and claim the closed linear operator is the infinitesimal generator of the bounded incompressible linear operator semigroup. We prove the existence and uniqueness of the solutions to the hyperbolic-elliptic coupled system by the semigroup theory