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

Authors:	Mingchu Gao

Institution:	(1) Department of Mathematics, Shanxi Teachers University, 041004 Linfen, P. R. China

Abstract:	In this paper, we first give a sufficient and necessary condition for $M = \left( {\begin{array}{{20}c} {A_1 } & I \\ {A_0 } & 0 \\ \end{array} } \right)$ to generate an exponentially bounded $\tilde C = \left( {\begin{array}{{20}c} C & 0 \\ 0 & C \\ \end{array} } \right)$ -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]. This project is supported by the NNSF of China, and the Youth Science and Technique Foundation of Shanxi Province, China

Keywords:	Abstract Cauchy problem C-semigroup C-wellposedness
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