Asymptotic analysis of abstract two-scale wave propagation problems

Sébastien Imperiale (1, 2)

1 Université Paris-Saclay
2 M3DISIM - Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine

This work addresses the mathematical analysis, by means of asymptotic analysis, of linear wave propagation problems involving two scales, represented by a single small parameter, and written in an abstract setting. This abstract setting is defined using linear operators in Hilbert spaces and also enters the framework of semi-group theory. In this setting, we show, under some assumptions on the structure of the wave propagation problems, weak and strong convergence of solutions with respect to the small parameter towards the solution of a well-defined limit problem.

Keywords: Wave equation; Asymptotic analysis; Operator theory

Domains: Analysis of PDEs [math.AP]

Sébastien Imperiale. Asymptotic analysis of abstract two-scale wave propagation problems. 2024. ⟨hal-03306856v2⟩