Some remarks on the essential spectrum of transport operators with abstract boundary conditions
Khalid Latrach
Source abstract
This article deals with the analysis of the essential spectrum of the one-dimensional transport operator with general boundary conditions where an abstract boundary operator relates the incoming and the outgoing fluxes. After a complete description of the spectrum of the transport equation with vacuum boundary conditions, sufficient conditions are given in terms of boundary and collision operators assuring the stability of the essential spectrum. The article ends with an analysis of the essential spectrum of the neutron transport operator in arbitrary dimension. Finally, some open problems are indicated.
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