ON AN UNBOUNDED LINEAR OPERATOR ARISING IN THE THEORY OF GROWING CELL-POPULATION

This paper deals with the spectral analysis of a class of unbounded li near operators corresponding to a partial differential equation origin ally proposed by J. L. Lebowitz and S. I. Rubinow (J. Math. Biol. 1, 1 974, 17-36) to model an age structured proliferating cell population. Individual cells are distinguished by age and cell cycle length. The c ell cycle length is considered as an inherited property determined at birth. After a detailed spectral analysis (for general boundary condit ions which model the process of cell division of mother cell and the i nherence of cycle length by daughter cells) it is shown that the assoc iated Cauchy problem is governed by a C-0-semigroup. A spectral decomp osition of the solutions into an asymptotic term and a transient one w hich will be estimated for smooth initial data is given. (C) 1997 Acad emic Press.