Publication: Asymptotic model of linearly visco-elastic Kelvin–Voigt type plates via Trotter theory
Issued Date
2019-12-01
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ISSN
16871847
16871839
16871839
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2-s2.0-85065918057
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Mahidol University
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SCOPUS
Bibliographic Citation
Advances in Difference Equations. Vol.2019, No.1 (2019)
Suggested Citation
Yotsawat Terapabkajornded, Somsak Orankitjaroen, Christian Licht Asymptotic model of linearly visco-elastic Kelvin–Voigt type plates via Trotter theory. Advances in Difference Equations. Vol.2019, No.1 (2019). doi:10.1186/s13662-019-2104-6 Retrieved from: https://repository.li.mahidol.ac.th/handle/20.500.14594/51215
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Title
Asymptotic model of linearly visco-elastic Kelvin–Voigt type plates via Trotter theory
Abstract
© 2019, The Author(s). 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.