SIAM J. on Mathematical Analysis

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Print: 0036-1410
Electronic: 1095-7145
Coden: SJMAAH

The SIAM Journal on Mathematical Analysis features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper should have content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biomathematics, mathematical physics, or to the computational analysis of such phenomena.

Featured Article

Inverse Transport with Isotropic Time-harmonic Sources

This paper concerns the reconstruction of the scattering coefficient in a two-dimensional transport equation from angularly averaged measurements when the probing source is isotropic and time-harmonic. This is a practical setting in the medical imaging modality called optical tomography. As the modulation frequency of the source increases, we show that the reconstruction of the scattering coefficient improves. More precisely, as the frequency $\omega$ increases, we show that all frequencies of the scattering coefficient lower than $b$ are reconstructed stably with an accuracy that improves as $\omega$ increases and $b$ decreases. The proofs are based on an analysis of the single scattering singularities of the transport equation and on careful analyses of oscillatory integrals by stationary phase arguments.

SIAM J. Math. Anal. 44, pp. 134-161