IJPAM: Volume 15, No. 4 (2004)
Department of Mathematics
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Abstract.In this paper, an operator approach is used for investigation of a birth-death process. First, an abstract evolution equation corresponding to the birth-death process with reflecting barriers formulated by differential equations with the initial conditions is established in an appropriate Banach space, and semigroup generation and spectral properties of the system operator associated with the evolution system are discussed. Based on the obtained results, the well-posedness of the system is concluded. Finally, the birth-death process with single channel is studied, and an asymptotic behavior of the system is explored and proved.
Received: June 26, 2004
AMS Subject Classification: 93C20, 35B35
Key Words and Phrases: birth-death process, well-posedness and stability, semigroup of linear operators
Source: International Journal of Pure and Applied Mathematics