| MAXIMAL SUBSPACES FOR SOLUTIONS OF THE SECOND ORDER ABSTRACT CAUCHY PROBLEM |
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| 作者姓名： | Guoxiang Chen Meiying Wang |
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| 作者单位： | Guoxiang Chen（Department of Applied Mathematics Audit University Nanjing 210029 P. R. China） ;
Meiying Wang（Department of Applied Mathematics Audit University Nanjing 210029 P. R. China） ; |
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| 摘 要： | For a continuous, increasing function ω: R → R \{0} of finite exponential type, this paper introduces the set Z(A, ω) of all x in a Banach space X for which the second order abstract differential equation (2) has a mild solution such that ω(t)]-1u(t,x) is uniformly continues on R , and show that Z(A, ω) is a maximal Banach subspace continuously embedded in X, where A ∈ B(X) is closed. Moreover, A|z(A,ω) generates an O(ω(t))strongly continuous cosine operator function family.
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| 关 键 词： | 柯西问题 余弦算子函数 最大子空间 Banach空间 |
| 收稿时间： | 10 February 2007 |
| 修稿时间： | 2007-02-10 |
Maximal subspaces for solutions of the second order abstract cauchy problem |
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| Guoxiang Chen Meiying Wang.MAXIMAL SUBSPACES FOR SOLUTIONS OF THE SECOND ORDER ABSTRACT CAUCHY PROBLEM[J].Analysis in Theory and Applications,2007,23(3):266-273. |
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| Authors: | Guoxiang Chen Meiying Wang |
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| Institution: | (1) Department of Applied Mathematics, Audit University, Nanjing, 210029, P. R. China |
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| Abstract: | For a continuous, increasing function ω: ℝ+ →ℝ+{0} of finite exponential type, this paper introduces the set Z(A, ω) of all x in a Banach space X for which the second order abstract differential equation (2) has a mild solution such that ω(t)]−1
u(t,x) is uniformly continues on ℝ+, and showthat Z(A, ω) is a maximal Banach subspace continuously embedded in X, where A ∈ B(X) is closed. Moreover, A|Z(A,ω) generates an O(ω(t)) strongly continuous cosine operator function family.
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| Keywords: | second order abstract cauchy problem solution with growth (э) cosine operator funcition family ABSTRACT CAUCHY PROBLEM SECOND ORDER SOLUTIONS SUBSPACES cosine operator family closed maximal Banach space subspace continuously embedded show mild solution second order abstract differential equation paper finite |
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