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

Leonard, A. (1971) Two-Dimensional Quarter Space Problems in One-Speed Transport Theory. Journal of Mathematical Physics, 12 (5). pp. 754-766. ISSN 0022-2488. doi:10.1063/1.1665644.

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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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Additional Information:© 1971 The American Institute of Physics. Received 20 July 1970. Part of this research was supported by a National Science Foundation Grant.
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Issue or Number:5
Record Number:CaltechAUTHORS:20120810-145444423
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Official Citation: Two-Dimensional Quarter Space Problems in One-Speed Transport Theory A. Leonard, J. Math. Phys. 12, 754 (1971), DOI:10.1063/1.1665644
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:33107
Deposited On:10 Aug 2012 22:40
Last Modified:09 Nov 2021 21:32

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