Acoustic diffraction problems on periodic graphs

作者：Rabinovich V S^*

来源：Functional Analysis and Its Applications, 2014, 48(4): 298-303.

DOI：10.1007/s10688-014-0074-8

• Helmholtz operators
• periodic graphs
• diffraction

We consider acoustic diffraction by graphs Gamma embedded in R-2 and periodic with respect to an action of the group 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 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.

• 出版日期2014-12