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Uniqueness of a solution and boundary conditions https://galprop.stanford.edu/forum/viewtopic.php?f=3&t=166 
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Author:  astrotula [ Fri Aug 30, 2013 7:18 pm ] 
Post subject:  Uniqueness of a solution and boundary conditions 
I'm curious to discuss such kind of general theoretical questions: what can be said about a uniqueness of a solution of the transport equation, which GALPROP looks for with boundary conditions specified? Was this question intentionally investigated? And what is the justification of the choice of boundary conditions? Saying by another words, why do we use specifically these boundary conditions? Particularly, it's slightly unclear for me how we can solve the equation without imposing anything for the momentum variable (as manual says)? What's about initial conditions? 
Author:  strong [ Sat Oct 26, 2013 11:32 pm ] 
Post subject:  Re: Uniqueness of a solution and boundary conditions 
The spatial boundary conditions are the standard assumptions of zero CR density at the halo boundaries. This is actually not very physical. Free escape at the boundaries (which is not the same thing) would be more appropriate. I am going to implement this soon. The momentum boundary conditions are indeed not rigorous, and GALPROP relies on the assumption that the momentum range is chosen large enough for this not to be important. At low energies with energy losses, the flow is only from high to low, so it is no problem. For reacceleration it could be a problem. Same for momentum advection. These issues deserve attention. 
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