中文摘要：

在新的初值条件下研究了一类双曲与椭圆耦合系统解的适定性，并且将解空间在半群的意义下进行扩展，使此类系统解的适定性有了全新的意义和性质．同时利用该系统解的适定性，使用双曲型伸缩技术，对松弛极限也进行了讨论．

英文摘要：

In this paper,the initial condition is considered for a class of hyperbolic and elliptic coupled system well posedness of the solution,and the solution space is extended in the semigroup sense,make the system well posedness of the meaning and nature of the new. At the same time,the well posedness of the solution of this system,the use of hyperbolic type expansion technology,discuss the relaxation limit of the system.