On a nonlinear version of Rotenberg model with infinite maturation velocities

Abstract

The present paper deals with a nonlinear boundary value problem derived from a model introduced by Rotenberg describing the growth of a cell population. Each cell of this population is distinguished by its degree of maturity and its maturation velocity . The biological boundary at and are fixed and tightly coupled through the mitosis. We present existence results for the problem in the case daughter cells and mother cells are related by a general reproduction rule and the maturation velocity is allowed to be infinite, i.e. . Our results are based on the classical topological fixed point theorems and use a compactness result established by below.

Keywords:

• nonlinear transport equation
• nonlinear boundary operator
• boundary value problem
• existence results

AMS Subject Classifications:

• 92B05
• 34B15
• 45K05

Notes

No potential conflict of interest was reported by the authors.