Operator-norm resolvent estimates for thin elastic periodically heterogeneous rods in moderate contrast

• Published in: Calculus of variations and partial differential equations Vol. 62; no. 5
• Main Authors: Cherednichenko, Kirill, Velčić, Igor, Žubrinić, Josip
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-06-2023; Springer Nature B.V
• Subjects: Analysis; Asymptotic properties; Calculus of Variations and Optimal Control; Optimization; Control; Estimates; Mathematical and Computational Physics; Mathematics; Mathematics and Statistics; Partial differential equations; Rods; Subspaces; Systems Theory; Theoretical; 35C20; 74K10; 35P15; 74B05; 74Q05
• ISSN: 0944-2669; 1432-0835
• DOI: 10.1007/s00526-023-02478-7

We provide resolvent asymptotics as well as various operator-norm estimates for the system of linear partial differential equations describing thin infinite elastic rods with material coefficients that rapidly oscillate along the rod. The resolvent asymptotics is derived simultaneously with respect to the rod thickness and the period of material oscillations, which are taken to be of the same order. The analysis is carried out separately on two invariant subspaces pertaining to the out-of-line and in-line displacements, under the assumption on material symmetries as well as in the general case when these two types of displacements are intertwined.