On the scattered field generated by a ball inhomogeneity of constant index
We consider the solution of a scalar Helmholtz equation where the potential (or index) takes two positive values, one inside a disk of radius $\epsilon$ and another one outside. We derive sharp estimates of the size of the scattered field caused by this disk inhomogeneity, for any frequencies and an...
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| Format: | Journal article |
| Language: | English |
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Society for Industrial and Applied Mathematics
2012
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| Summary: | We consider the solution of a scalar Helmholtz equation where the potential (or index) takes two positive values, one inside a disk of radius $\epsilon$ and another one outside. We derive sharp estimates of the size of the scattered field caused by this disk inhomogeneity, for any frequencies and any contrast. We also provide a broadband estimate, that is, a uniform bound for the scattered field for any contrast, and any frequencies outside of a set which tend to zero with $\epsilon$. |
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