On the limiting amplitude principle for the wave equation with variable coefficients
| Autor: | Arnold, Anton, Geevers, Sjoerd, Perugia, Ilaria, Ponomarev, Dmitry |
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| Přispěvatelé: | Vienna University of Technology (TU Wien), University of Vienna [Vienna], Analyse fonctionnelle pour la conception et l'analyse de systèmes (FACTAS), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), St. Petersburg Department of V.A. Steklov Mathematical Institute (PDMI RAS), Steklov Mathematical Institute [Moscow] (SMI), Russian Academy of Sciences [Moscow] (RAS)-Russian Academy of Sciences [Moscow] (RAS) |
| Rok vydání: | 2022 |
| Předmět: |
[PHYS.PHYS.PHYS-OPTICS]Physics [physics]/Physics [physics]/Optics [physics.optics]
FOS: Physical sciences [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA] Numerical Analysis (math.NA) Mathematical Physics (math-ph) [PHYS.MECA.ACOU]Physics [physics]/Mechanics [physics]/Acoustics [physics.class-ph] Computer Science::Other Mathematics - Analysis of PDEs [NLIN.NLIN-PS]Nonlinear Sciences [physics]/Pattern Formation and Solitons [nlin.PS] FOS: Mathematics 35L05 35L10 35B10 35B40 [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] [NLIN.NLIN-SI]Nonlinear Sciences [physics]/Exactly Solvable and Integrable Systems [nlin.SI] Mathematics - Numerical Analysis Mathematical Physics Analysis of PDEs (math.AP) |
| DOI: | 10.48550/arxiv.2202.10105 |
| Popis: | In this paper, we prove new results on the validity of the limiting amplitude principle (LAP) for the wave equation with nonconstant coefficients, not necessarily in divergence form. Under suitable assumptions on the coefficients and on the source term, we establish the LAP for space dimensions 2 and 3. This result is extended to one space dimension with an appropriate modification. We also quantify the LAP and thus provide estimates for the convergence of the time-domain solution to the frequency-domain solution. Our proofs are based on time-decay results of solutions of some auxiliary problems. The obtained results are illustrated numerically on radially symmetric problems in dimensions 1,2 and 3. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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