C-wellposedness of the complete second order abstract cauchy problem and applications

In this paper, we first give a sufficient and necessary condition for M=(A1A0I0) to generate an exponentially bounded C~=(C00C)-semigroup and discuss its relations to the C-wellposedness of the complete second order abstract Cauchy problem ((ACP2) for short) in some sense. Then we use these results and those in [1] to discuss the C-(exponential) wellposedness of a kind of (ACP2) with application backgrounds, and develop the results in [2].