<div class="csl-bib-body">
<div class="csl-entry">Arnold, A., Geevers, S., Perugia, I., & Ponomarev, D. (2024). On the limiting amplitude principle for the wave equation with variable coefficients. <i>Communications in Partial Differential Equations</i>. https://doi.org/10.1080/03605302.2024.2341070</div>
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dc.identifier.issn
0360-5302
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/197077
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dc.description.abstract
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.
en
dc.language.iso
en
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dc.publisher
TAYLOR & FRANCIS INC
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dc.relation.ispartof
Communications in Partial Differential Equations
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dc.subject
wave equation
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dc.subject
variable coefficients
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dc.subject
limiting amplitude principle
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dc.subject
long-time asymptotics
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dc.title
On the limiting amplitude principle for the wave equation with variable coefficients
