This article is cited in 3 papers

Determination of a diffuse reflecting surface under pulsed irradiation

V. A. Kan^ab, I. V. Prokhorov<sup>ab

a</sup> Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, Vladivostok
^b Far Eastern Federal University, Vladivostok

Abstract: An inverse problem of determining a diffusely reflecting surface under given functionals of the radiation flux density for a nonstationary radiation transfer equation is considered. Assuming the point pulsed source and the single scattering approximation, authors obtained the nonlinear differential equation. The solution has been obtained in a few quadratures to determine the profile of the Lambert surface. The computational experiments were carried out on test examples.

Key words: radiation transfer equation, diffuse reflection, Lambert's cosine law, inverse problem.

UDC: 517.958

MSC: Primary 35Q20; Secondary 35Q60

Received: 01.11.2018