SOLVABILITY AND WELL-POSEDNESS OF HIGHERORDER ABSTRACT CAUCHY PROBLEMS

作     者：郑权 

作者机构：Department of Mathematics Huazhong University of Science and Technology Wuhan 430074 PRC 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：1991年第34卷第2期

页      面：147-156页

核心收录：

学科分类：07[理学] 08[工学] 0701[理学-数学] 

主　　题：higher-order abstract Cauchy problems solvability well-posedness C₀ semigroup vector valued Laplace transform. 

摘      要：We consider the higher-order Cauchy problem （ACPn） xn（t）=sum from i=0 to n-1 Bixi（t）1xi（0）=xi for 0≤i≤n-1,where Bi（0≤i≤n-1） are closed linear operators on a Banach space X such that D=∩ i=0 n-1 D（Bi）is dense in X. It is well known that the solvability and the well-posedness of （ACPn）were studied only in some special cases, such as D(Bn-1)?D（Bi） for 0≤i≤n-2 by F. Neu-brander and a factoring case by J. T. Sandefur. In this paper, by using some new results ofvector valued Laplace transforms given by W. Arenddt, we obtain some characterizations ofthe solvability and some sufficiency conditions of the well-posedness for general （ACPn）,which generalize F. Neubrander’s results and the famous results for （ACP1）