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December  2017, 10(4): 957-976. doi: 10.3934/krm.2017038

## Grossly determined solutions for a Boltzmann-like equation

 Department of Mathematics, Bradley University, Bradley Hall 445, Peoria, IL 61625, USA

Received  October 2015 Revised  December 2016 Published  March 2017

Fund Project: The author is supported by NSF grant DMS 08-38434 "EMSW21-MCTP: Research Experience for Graduate Students" and from the Caterpillar Fellowship Grant at Bradley University.

In gas dynamics, the connection between the continuum physics model offered by the Navier-Stokes equations and the heat equation and the molecular model offered by the kinetic theory of gases has been understood for some time, especially through the work of Chapman and Enskog, but it has never been established rigorously. This paper established a precise bridge between these two models for a simple linear Boltzman-like equation. Specifically a special class of solutions, the grossly determined solutions, of this kinetic model are shown to exist and satisfy closed form balance equations representing a class of continuum model solutions.

Citation: Thomas Carty. Grossly determined solutions for a Boltzmann-like equation. Kinetic & Related Models, 2017, 10 (4) : 957-976. doi: 10.3934/krm.2017038
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##### References:
The graph of $|\boldsymbol{\xi}|=\Xi(c)$
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