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标题：Asymptotic model of linearly visco-elastic Kelvin–Voigt type plates via Trotter theory
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作者：Yotsawat Terapabkajornded ; Somsak Orankitjaroen ; Christian Licht 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2019
卷号：2019
期号：1
页码：1-9
DOI：10.1186/s13662-019-2104-6
出版社：Hindawi Publishing Corporation
摘要：We confirm the study (Licht in C. R., Méc. 341:697–700, 2013) devoted to the quasi-static response for a visco-elastic Kelvin–Voigt plate whose thickness goes to zero. For each thickness parameter, the quasi-static response is given by a system of partial differential equations with initial and boundary conditions. Reformulating scaled systems into a family of evolution equations in Hilbert spaces of possible states with finite energy, we use Trotter theory of convergence of semi-groups of linear operators to identify the asymptotic behavior of the system. The asymptotic model we obtain and the genuine one have the same structure except an occurrence of a new state variable. Eliminating the new state variable from our asymptotic model leads to the asymptotic model in (Licht in C. R., Méc. 341:697–700, 2013) which involves an integro-differential system.
关键词：Asymptotic model ; Thin visco-elastic plates ; Kelvin–Voigt visco-elasticity ; Trotter theory