Radiation condition at infinity for the high-frequency Helmholtz equation: optimality of a non-refocusing criterion (Q482844)
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scientific article
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| English | Radiation condition at infinity for the high-frequency Helmholtz equation: optimality of a non-refocusing criterion |
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Radiation condition at infinity for the high-frequency Helmholtz equation: optimality of a non-refocusing criterion (English)
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6 January 2015
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The purpose of this article is to study the rescaled Helmholtz equation containing the space-dependent refraction index \(n^2(x), x\in\mathbb{R}^d\). The asymptotic analysis of the repealed Helmholtz equation is done by transformation to a time-dependent problem. The main part of the paper is concerned with the construction of a refraction index, which is both nontrapping and violates the non-refocusing condition. This is done by constructing the mathematical reflection set in dimension \(d\). The proofs use distribution theory.
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high-frequency Helmholtz equation
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radiation condition at infinity
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pseudodifferential operator
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stationary phase theorem
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