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Application of the albedo shifting method to an integral equation. (Russian, English) Zbl 1064.45003
Zh. Vychisl. Mat. Mat. Fiz. 42, No. 6, 905-912 (2002); translation in Comput. Math. Math. Phys. 42, No. 6, 870-877 (2002).
The following conservative integral equation on the semi-axes is considered \[ f(x) = g(x) + \int_0^{+\infty}K(| x - t| )f(t)\,dt + \int_0^{+\infty}K_0(x + t)f(t)\,dt, \] where the kernels \(K\) and \(K_0\) are superposition of exponents and present a sum and a remainder of arguments. Having applied the special factorization method by N. B. Engibaryan and the author [ibid. 38, No. 3, 466–482 (1998; Zbl 0949.45004)], which is an analog of the albedo shifting method, the conservative problem is reduced to a dissipative one. The solvability of the equation and the existence of a solution at infinity are proved.

45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
47A68 Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators
82C40 Kinetic theory of gases in time-dependent statistical mechanics
85A25 Radiative transfer in astronomy and astrophysics