Abstract
We consider acoustic diffraction by graphs Γ embedded in ℝ2 and periodic with respect to an action of the group ℤn, n = 1, 2. The diffraction problem is described by the Helmholtz equation with variable nonperiodic bounded coefficients and nonperiodic transmission conditions on the graph Γ. We introduce single and double layer potentials on Γ generated by the Schwartz kernel of the operator inverse to the Helmholtz operator on ℝ2 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.
Original language | English |
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Pages (from-to) | 298-303 |
Number of pages | 6 |
Journal | Functional Analysis and its Applications |
Volume | 48 |
Issue number | 4 |
DOIs | |
State | Published - 17 Dec 2014 |
Keywords
- Helmholtz operators
- diffraction
- periodic graphs