摘要
This paper is concerned with applications of integrated semigroups tothe following Cauchy problem:（ACP<sub>n</sub>） x<sup>n</sup>（t）=sum from i=0 to n-1 B<sub>i</sub>x<sup>i</sup>（t）,x<sup>i</sup>（0）=x<sub>i</sub>,0（?）i（?）n-1where B<sub>i</sub> （0（?）i（?）n-1） are closed linear operators on a Banach space X.Auniqueness theorem,a condition of the solvability,a condition of the exponentialwell-posedness,and some results for the special case that B<sub>n-1</sub> is bounded andD(B<sub>n-2</sub>)（?）D（B<sub>i</sub>）（0（?）i（?）n-3） are obtained.
This paper is concerned with applications of integrated semigroups tothe following Cauchy problem:(ACP_n) x^(n)(t)=sum from i=0 to n-1 B_ix^(i)(t),x^(i)(0)=x_i,0(?)i(?)n-1where B_i (0(?)i(?)n-1) are closed linear operators on a Banach space X.Auniqueness theorem,a condition of the solvability,a condition of the exponentialwell-posedness,and some results for the special case that B_(n-1) is bounded andD(B_(n-2))(?)D(B_i)(0(?)i(?)n-3) are obtained.
基金
This project was supported by the National Science Foundation of China
