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On the Spectrum of a One-Velocity Transport Operator with Maxwell Boundary Condition

โœ Scribed by Zhang Xianwen; Liang Benzhong

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
194 KB
Volume
202
Category
Article
ISSN
0022-247X

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โœฆ Synopsis

The spectrum of a one-velocity transport operator with Maxwell boundary condition is discussed in L 1 space. First, it is proved that the spectrum of a streaming operator associated with the transport operator consists of infinitely isolated eigenvalues, each of which is simple; furthermore, a formula for computation of these eigenvalues is obtained. Second, it is proved that the essential spectrum of the transport operator is empty and it is pointed out that the dominant eigenvalue of the transport operator exists. Finally, a necessary and sufficient condition for the existence of a complex eigenvalue of the transport operator in a right half plane is given.

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