Polynomial growth dynamics of telomere loss in a heterogeneous cell population. Arino, O., Sánchez, E., & Webb, G. F. Dynam. Contin. Discrete Impuls. Systems, 3(3):263–282, 1997. abstract bibtex The authors derive a variation of parameters formula for the equation $x'(t)=L(x\sb t)+f(t)$, where $L:C([-r,0],E)\to E$ is a bounded linear operator, $E$ is a Banach space and $x\sb t(\theta)=x(t+\theta), \theta ∈[-r,0]$. They use a decomposition of the space $C([-r,0],E)$ with respect to the spectrum of a generator of a solution semigroup for the homogeneous problem to obtain a decomposition of the solution and corresponding projectors.
@Article{ArinoSanchezWebb1997,
author = {Arino, Ovide and S{\'a}nchez, E. and Webb, G. F.},
title = {Polynomial growth dynamics of telomere loss in a heterogeneous cell population},
journal = {Dynam. Contin. Discrete Impuls. Systems},
year = {1997},
volume = {3},
number = {3},
pages = {263--282},
issn = {1201-3390},
abstract = {The authors derive a variation of parameters formula
for the equation $x'(t)=L(x\sb t)+f(t)$, where
$L:C([-r,0],E)\to E$ is a bounded linear operator,
$E$ is a Banach space and $x\sb
t(\theta)=x(t+\theta), \theta \in [-r,0]$. They use
a decomposition of the space $C([-r,0],E)$ with
respect to the spectrum of a generator of a solution
semigroup for the homogeneous problem to obtain a
decomposition of the solution and corresponding
projectors.},
classmath = {*34K30 Functional-differential equations in abstract spaces 47D06 One-parameter semigroups and linear evolution equations },
coden = {DCDIS},
fjournal = {Dynamics of Continuous, Discrete and Impulsive Systems. An International Journal for Theory and Applications},
keywords = {functional differential equation; variation of parameters formula; fundamental solution; spectral decomposition},
mrclass = {92D25 (47D06 47N60 92C40)},
mrnumber = {99c:92032},
mrreviewer = {S. K. Chatterjea},
reviewer = {H.Petzeltova (Praha)},
}
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