完全二阶抽象Cauchy问题的C-适定性及其应用

C-wellposedness of the Complete Second Order Abstract Cauchy Problem and applications

在本文中,我们给出了算子矩阵生成指数有界的半群的充分必要条件，其中A0，A1为完全二阶抽象柯西问题（ACP2）的系数算子，并讨论了它与（ACP2）在某种意义下的C-适定性之间的关系．最后，我们应用此结果及［3］中的结论讨论了一类具有应用背景的完全二阶抽象柯西问题的C-适定性．

In this paper, we give sufficient and necessary conditions for operator ma trix to generate an exponentially bounded semigroup, where A1 and A0 are the coefficent operators of the complete sedond order abstract Cauchy problem (ACP2). we also give the relationship between the fact that generates an exponentially bounded semigroup and the C-wellposedness of semigroup and the C-wellposedness of (ACP2). Finally, we apply these,esult and those in [3] to discuss the C-wellposedness of a kind of (ACP2) with application background.