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Some convolution-type integral equations in kinetic theory. (English. Russian original) Zbl 0949.45004

Comput. Math. Math. Phys. 38, No. 3, 452-467 (1998); translation from Zh. Vychisl. Mat. Mat. Fiz. 38, No. 3, 466-482 (1998).
The conservative Wiener-Hopf integral equation, whose kernel is an even function that is a superposition of exponential functions, is considered. A generalization of this equation is analyzed. It is proved that the limits of the solutions to these equations as \(x\) approaches \(+\infty\) exist. These limits are evaluated in terms of the Ambartsumyan function. The results are applied to problems in the kinetic theory of gases and radiative transfer theory.

MSC:

45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
82C40 Kinetic theory of gases in time-dependent statistical mechanics
85A25 Radiative transfer in astronomy and astrophysics
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