EXISTENCE RESULTS FOR A BOUNDARY VALUE PROBLEM ARISING IN GROWING CELL POPULATIONS

Abstract

The aim of this article is to prove some results regarding the existence of solutions on L 1 spaces to a nonlinear boundary value problem derived from a model introduced by Rotenberg (1983) describing the growth of a cell population. Each cell of this population is distinguished by two parameters: its degree of maturity μ and its maturation velocity v. The biological boundary of μ = 0 and μ = a (a > 0) are fixed and tightly coupled through the mitosis. At mitosis, daughter cells and mother cells are related by a general reproduction rule which covers all known biological ones. Our proofs, based on topological methods, use essentially the specific properties of weakly compact sets on L 1 spaces.