Analyticity of the Sine Family with L^P-Maximal Regularity for Second Order Cauchy Problems  

作　　者：Yong Zhong HUANG Meng Cheng WANG 

机构地区：[1]School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2010年第3期561-568,共8页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China (Grant No. 10672062)

摘　　要：If the second order problem u（t） ＋ Bu（t） ＋ Au（t） = f（t）, u（0） =u（0） = 0 has L^p-maximal regularity, 1 〈 p 〈 ∞, the analyticity of the corresponding propagator of the sine type is shown by obtaining the estimates of ‖λ（λ^2 ＋ λB ＋ A）^-1‖ and ‖B（λ^2 ＋ λB ＋ A）^-1‖ for λ∈ C with Reλ 〉 ω, where the constant ω≥ 0.If the second order problem u（t） ＋ Bu（t） ＋ Au（t） = f（t）, u（0） =u（0） = 0 has L^p-maximal regularity, 1 〈 p 〈 ∞, the analyticity of the corresponding propagator of the sine type is shown by obtaining the estimates of ‖λ（λ^2 ＋ λB ＋ A）^-1‖ and ‖B（λ^2 ＋ λB ＋ A）^-1‖ for λ∈ C with Reλ 〉 ω, where the constant ω≥ 0.

关 键 词：ANALYTICITY second order Cauchy problem maximal regularity PROPAGATOR 

分 类 号：O175.1[理学—数学] TG823[理学—基础数学]