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Funktsional. Anal. i Prilozhen., 2014, Volume 48, Issue 4, Pages 77–83 (Mi faa3168)  

This article is cited in 1 scientific paper (total in 1 paper)

Brief communications

Acoustic Diffraction Problems on Periodic Graphs

V. S. Rabinovich

Instituto Politecnico Nacional, ESIME–Zacatenco

Abstract: We consider acoustic diffraction by graphs $\Gamma$ embedded in $\mathbb{R}^{2}$ and periodic with respect to an action of the group $\mathbb{Z}^{n}$, $n=1,2$. The diffraction problem is described by the Helmholtz equation with variable nonperiodic bounded coefficients and nonperiodic transmission conditions on the graph $\Gamma$. We introduce single and double layer potentials on $\Gamma$ generated by the Schwartz kernel of the operator inverse to the Helmholtz operator on $\mathbb{R}^{2}$ and reduce the diffraction problem to a boundary pseudodifferential equation on the graph. Necessary and sufficient conditions for the boundary operators to be Fredholm are obtained.

Keywords: Helmholtz operators, periodic graphs, diffraction

Funding Agency Grant Number
National System of Researchers in Mexico (SNI)
CONACYT - Consejo Nacional de Ciencia y Tecnología 000000000179872


DOI: https://doi.org/10.4213/faa3168

Full text: PDF file (203 kB)
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English version:
Functional Analysis and Its Applications, 2014, 48:4, 298–303

Bibliographic databases:

UDC: 517.9
Received: 22.11.2012

Citation: V. S. Rabinovich, “Acoustic Diffraction Problems on Periodic Graphs”, Funktsional. Anal. i Prilozhen., 48:4 (2014), 77–83; Funct. Anal. Appl., 48:4 (2014), 298–303

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. M. Erusalimskyi, “2–3 Paths in a Lattice Graph: Random Walks”, Math. Notes, 104:3 (2018), 395–403  mathnet  crossref  crossref  isi  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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