Two-Dimensional Quarter Space Problems in One-Speed Transport Theory

Abstract

Methods derived from the theory of several complex variables are used as a means of analyzing a class of two‐dimensional transport problems in a scattering and absorbing quarter space (0 ≤ x_1, 0 ≤ x_2, −∞ ≤ x_3 ≤ ∞) described by a linear, one‐speed Boltzmann equation. Using Fourier transformation and the Bochner decomposition, the multivariable analog of the Wiener‐Hopf factorization, we find the Green's function in transform space, which solves all source problems having a solution bounded at infinity. The transform of the density asymptotically far from the corner (x_1 = x_2 = 0) is determined explicitly, while the remainder is given in terms of the solution to a pair of Fredholm equations.

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