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Asymptotic Analysis - Volume 134, issue 1-2

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Price: EUR 420.00
ISSN 0921-7134 (P)
ISSN 1875-8576 (E)

Impact Factor 2024: 1.1

The journal Asymptotic Analysis fulfills a twofold function. It aims at publishing original mathematical results in the asymptotic theory of problems affected by the presence of small or large parameters on the one hand, and at giving specific indications of their possible applications to different fields of natural sciences on the other hand. 

Asymptotic Analysis thus provides mathematicians with a concentrated source of newly acquired information which they may need in the analysis of asymptotic problems.

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Asymptotic expansion of solutions to the wave equation with space-dependent damping

Authors: Sobajima, Motohiro | Wakasugi, Yuta

Article Type: Research Article

Abstract: We study the large time behavior of solutions to the wave equation with space-dependent damping in an exterior domain. We show that if the damping is effective, then the solution is asymptotically expanded in terms of solutions of corresponding parabolic equations. The main idea to obtain the asymptotic expansion is the decomposition of the solution of the damped wave equation into the solution of the corresponding parabolic problem and the time derivative of the solution of the damped wave equation with certain inhomogeneous term and initial data. The estimate of the remainder term is an application of weighted energy methods … Show more

Keywords: Wave equation, space-dependent damping, asymptotic expansion

DOI: 10.3233/ASY-231834

Citation: Asymptotic Analysis, vol. 134, no. 1-2, pp. 241-279, 2023

Price: EUR 27.50

A note on local energy decay results for wave equations with a potential

Authors: Ikehata, Ryo

Article Type: Research Article

Abstract: In this paper, we derive uniform local energy decay results for wave equations with a short-range potential in an exterior domain. In this study, we considered this problem within the framework of non-compactly supported initial data, unlike previously reported studies. The essential parts of analysis are both L 2 -estimates of the solution itself and the weighted energy estimates. Only a multiplier method is used, and we do not rely on any resolvent estimates.

Keywords: Wave equation, short-range potential, exterior mixed problem, non-compact support, initial data, local energy, algebraic decay

DOI: 10.3233/ASY-231835

Citation: Asymptotic Analysis, vol. 134, no. 1-2, pp. 281-295, 2023

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