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Conference Papers Year : 2022

Revisiting the limiting amplitude principle for the wave equation with variable coefficients

Abstract

The limiting amplitude principle is a well-known result connecting the solution of the Helmholtz equation with the large-time behavior of timedependent wave equations with a source term which is periodic in time. Motivated by numerical analysis of time-domain methods for stationary scattering problems in heterogeneous media, we quantify the solution convergence of such time-dependent wave equation towards the stationary solution, under some assumptions on the coefficients and the source term. We also generalise the formulation of the limiting amplitude principle to the one-dimensional setting where the classical statement of the principle is known to be violated.
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Dates and versions

hal-03925536 , version 1 (05-01-2023)

Identifiers

  • HAL Id : hal-03925536 , version 1

Cite

Anton Arnold, Sjoerd Geevers, Ilaria Perugia, Dmitry Ponomarev. Revisiting the limiting amplitude principle for the wave equation with variable coefficients. Waves 2022, Jul 2022, Palaiseau, France. ⟨hal-03925536⟩
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