Well-posedness of a nonlinear evolution equation arising in growing cell population

Abstract

Communicated by M. LachowiczWe prove that a nonlinear evolution equation which comes from a model of an age-structured cell population endowed with general reproduction laws is well-posed.

An existence and uniqueness principle for a nonlinear version of the Lebowitz‐Rubinow model with infinite maximum cycle length

“…Hence, at mitosis, daughter and mother cells are related by a nonlinear rule, which describes the boundary conditions. It writes in the shape f ( t ,0, l )=[ R f ( t ,·,·)]( l ), where R denotes a nonlinear operator on suitable trace spaces and is intended to model the transition from mother cells with cycle length l to daughter cells with cycle length l …”

“…Thus, we can consider the following nonlinear problem: We point out that in García‐Falset the well‐posedness of problem was discussed in the space L 1 when the maximum cycle length is finite for local boundary conditions. Later, in Al‐Izeri and Latrach, they completed the above study showing that problem , when , has a unique mild solution in L p ‐spaces with .…”

“…We close this introduction by noticing that this work and the ideas of proofs of our results are inspired by the papers …”

A Nonlinear Age-Structured Model of Population Dynamics with Inherited Properties

“…This paper is inspired and motivated by the work [8] where the wellposedness of Problem (1.1)-(1.2) was discussed in the space L 1 . This work is intended to complete the results obtained in [8]. We prove that Problem (1.1)-(1.2) has a unique mild solution in L p -spaces with 1 < p < ∞.…”