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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

A nonlinear Boltzmann equation in transport theory


Author: C. V. Pao
Journal: Trans. Amer. Math. Soc. 194 (1974), 167-175
MSC: Primary 82.45
DOI: https://doi.org/10.1090/S0002-9947-1974-0347294-8
MathSciNet review: 0347294
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Abstract: The method of successive approximations is used to show the existence of a unique solution to a model of a nonlinear Boltzmann equation under the homogeneous boundary and typical initial conditions. An explicit formula in terms of the prescribed functions for the calculation of an approximate solution and its error estimate are given. This formula reveals an interesting analogy between the initial-boundary value problem of the Boltzmann equation and the Cauchy problem for ordinary differential equations. Numerical results for approximate solutions of the problem can be computed by using a computer. The linear Boltzmann equation is considered as a special case and a similar formula for the calculation of approximate solutions is included.


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DOI: https://doi.org/10.1090/S0002-9947-1974-0347294-8
Keywords: Boltzmann equations, neutron transport problems, initial-boundary value problems, successive approximations, existence and uniqueness of a solution, operator equations
Article copyright: © Copyright 1974 American Mathematical Society