Analyticity of the sine family with Lp-maximal regularity for second order Cauchy problems

If the second order problem ü ( t )+ B ( t )+ Au ( t ) = f ( t ), u (0) = (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 wi...

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Bibliographic Details
Published inActa mathematica Sinica. English series Vol. 26; no. 3; pp. 561 - 568
Main Authors Huang, Yong Zhong, Wang, Meng Cheng
Format Journal Article
LanguageEnglish
Published Heidelberg Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 2010
Subjects
Mathematics
Mathematics and Statistics
35G10
35B65
35Q99
propagator
second order Cauchy problem
analyticity
maximal regularity
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Summary:If the second order problem ü ( t )+ B ( t )+ Au ( t ) = f ( t ), u (0) = (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 Re λ > ω , where the constant ω ≥ 0.
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-010-7440-0