Leonard, A. (1971) TwoDimensional Quarter Space Problems in OneSpeed Transport Theory. Journal of Mathematical Physics, 12 (5). pp. 754766. ISSN 00222488. http://resolver.caltech.edu/CaltechAUTHORS:20120810145444423

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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.
Item Type:  Article  

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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.  
Group:  GALCIT  
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Record Number:  CaltechAUTHORS:20120810145444423  
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:20120810145444423  
Official Citation:  TwoDimensional Quarter Space Problems in OneSpeed 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  
Collection:  CaltechAUTHORS  
Deposited By:  Aucoeur Ngo  
Deposited On:  10 Aug 2012 22:40  
Last Modified:  20 Sep 2016 20:54 
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