完全二阶抽象 Cauchy 问题的 Mild C-适定性

MILD C WELLPOSEDNESS OF THE COMPLETE SECOND ORDER ABSTRACT CAUCHY PROBLEM

我们给出了算于矩阵Ｎ＝０ＩＡ０Ａ１（或其某扩张）生成指数有界的Ｃ＝Ｃ００Ｃ－半群的Ｈｉｌｅ－Ｙｏｓｉｄａ型充要条件。之后，我们由此给出完全二阶Ｃａｕｃｈｙ问题ｍｉｌｄＣ－指数适定性的充要的Ｈｉｌｅ－Ｙｏｓｉｄａ型的条件。

This paper is devoted to the discussion of mild C wellposedness of the complete second order abstract Cauchy problem. In section I, we first give the definition of mild C wellposedness of the complete second order abstract Cauchy problem, which is denoted by (ACP 2). We also discuss the relationship of the mild C wellposedness of (ACP 2) to the existence of a mild C￣=CO OC existence family for N=OI A 0A 1 in section 1. Finally, in section 1, we give a Hille Yosida type theorem of sufficient and necessary conditions for N=OI A 0A 1(or its entension) to generate an exponentially bounded C￣ semigroup. In section 2, we discuss the (mild) C exponential wellpozedness of (ACP 2). First, we give the equivalent relationship of the exponentially bounded mild C existence family for operator A with the mild C exponential wellpozedness of the first order abstract Cauchy problem, develop the nesult in . Then, using the result above, we give the relationship of the fact that N genevates an exponentially bounded C￣ semigroup and the mild C exponential wellposedness of (ACP 2).