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Journal of Function Spaces
Volume 2014 (2014), Article ID 748792, 10 pages
http://dx.doi.org/10.1155/2014/748792
Research Article

Spectral Distribution of Transport Operator Arising in Growing Cell Populations

Department of Mathematics, Shangrao Normal University, Shangrao, Jiangxi 334001, China

Received 27 May 2014; Accepted 12 August 2014; Published 25 August 2014

Academic Editor: Leszek Olszowy

Copyright © 2014 Hongxing Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Transport equation with partly smooth boundary conditions arising in growing cell populations is studied in space. It is to prove that the transport operator generates a semigroup and the ninth-order remainder term of the Dyson-Phillips expansion of the semigroup is compact, and the spectrum of transport operator consists of only finite isolated eigenvalues with finite algebraic multiplicities in a trip . The main methods rely on theory of linear operators, comparison operators, and resolvent operators approach.