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

A. Leonard
1971 Journal of Mathematical Physics  
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 , -oo ~ x 8 ~ oo) 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
more » ... 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. lm k. J i:t. J k. plane J ---------+ ---------Re k. J -------t ----+ ~+ "j i3. J FIG. 2. integration paths in the tubular domain T.
doi:10.1063/1.1665644 fatcat:majvn4uf4vbpjmut46iptkx7li