Operator Aspects of Wave Propagation Through Periodic Media

Kirill Cherednichenko () and Yi-Sheng Lim ()
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Kirill Cherednichenko: University of Bath, Department of Mathematical Sciences
Yi-Sheng Lim: Texas A&M University, Department of Mathematics

Chapter 110 in Operator Theory, 2026, pp 3467-3512 from Springer

Abstract: Abstract Recent results in quantitative homogenization of the wave equation with rapidly oscillating coefficients are discussed from the operator-theoretic perspective, which views the solution as the result of applying the operator of hyperbolic dynamics, i.e., the unitary group of a self-adjoint operator on a suitable Hilbert space. A prototype one-dimensional example of utilizing the framework of Ryzhov boundary triples is analyzed, where operator-norm resolvent estimates for the problem of classical moderate-contrast homogenization are obtained. By an appropriate “dilation” procedure, these are shown to upgrade to second-order (and more generally, higher order) estimates for the resolvent and the unitary group describing the evolution for the related wave equation.

Keywords: Homogenization; Resolvent asymptotics; Wave propagation; Hyperbolic evolution; 35P15; 35C20; 74B05; 74Q05 (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-3-032-16356-1_78

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