Determination of the absorption coefficient in the spherically symmetric case. (English. Russian original) Zbl 0796.76075

Gryn’, V. I.

U.S.S.R. Comput. Math. Math. Phys. 30, No. 5, 42-54 (1990); translation from Zh. Vychisl. Mat. Mat. Fiz. 30, No. 9, 1341-1356 (1990).

Summary: The problem of determining the absorption coefficient of a radiative non- diffusive gas, given the incoming and outgoing radiation and assuming spherical symmetry, is replaced by an equivalent nonlinear Volterra integral equation of the second kind. The existence, uniqueness and stability of the solutions of this problem in the first and second volume-luminescence approximation are considered, confining our attention to the class of continuous absorption coefficients.

MSC:

76N15	Gas dynamics (general theory)
85A25	Radiative transfer in astronomy and astrophysics
45D05	Volterra integral equations

Keywords:

radiative non-diffusive gas; nonlinear Volterra integral equation of the second kind; existence; uniqueness; stability; volume-luminescence approximation