ASYMPTOTIC ANALYSIS OF A CLASS OF ABSTRACT STIFF WAVE PROPAGATION PROBLEMS

Sebastien Imperiale

doi:10.1137/24M1679458

ASYMPTOTIC ANALYSIS OF A CLASS OF ABSTRACT STIFF WAVE PROPAGATION PROBLEMS

Sebastien Imperiale

INRIA

Research output: Contribution to journal › Article › peer-review

Abstract

This work addresses the mathematical analysis, by means of asymptotic analysis, of a class of linear wave propagation problems with singular stiff terms represented by a single small parameter. This abstract setting is defined using linear operators in Hilbert spaces. 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.

Original language	English
Pages (from-to)	1389-1416
Number of pages	28
Journal	Multiscale Modeling and Simulation
Volume	23
Issue number	3
DOIs	https://doi.org/10.1137/24M1679458
Publication status	Published - 1 Jan 2025
Externally published	Yes

Keywords

asymptotic analysis
operator theory
wave equation

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10.1137/24M1679458

Cite this

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abstract = "This work addresses the mathematical analysis, by means of asymptotic analysis, of a class of linear wave propagation problems with singular stiff terms represented by a single small parameter. This abstract setting is defined using linear operators in Hilbert spaces. 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.",

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N2 - This work addresses the mathematical analysis, by means of asymptotic analysis, of a class of linear wave propagation problems with singular stiff terms represented by a single small parameter. This abstract setting is defined using linear operators in Hilbert spaces. 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.

AB - This work addresses the mathematical analysis, by means of asymptotic analysis, of a class of linear wave propagation problems with singular stiff terms represented by a single small parameter. This abstract setting is defined using linear operators in Hilbert spaces. 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.

KW - asymptotic analysis

KW - operator theory

KW - wave equation

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ASYMPTOTIC ANALYSIS OF A CLASS OF ABSTRACT STIFF WAVE PROPAGATION PROBLEMS

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Keywords

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