Time asymptotic behaviour for unbounded linear operator arising in growing cell populations

This paper is concerned with the spectral analysis of a class of unbounded, linear operators, originally proposed by M. Rotenberg (J. Theor. Biol. 96 (1982) 495; J. Theor. Biol. 103 (1983) 18 1). After a detailed spectral analysis it is shown that the associated Cauchy problem is governed by a C-0-semigroup. Next, we discuss the irreducibility of the transport semigroup. In particular, we show that the transport semigroup is irreducible if the boundary operator is strictly positive. Finally, a spectral decomposition of the solutions into an asymptotic term and a transient one which will be estimated for smooth initial data is given. (C) 2003 Elsevier Science Ltd. All rights reserved.