On the solutions for a nonlinear boundary value problem modeling a proliferating cell population with inherited cycle length

Al-Izeri, Abdul-Majeed; Latrach, Khalid

doi:10.1016/j.na.2016.05.001

Cited by 3 publications

(1 citation statement)

References 21 publications

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“…We note that a stationary version of problem was discussed in the space L 1 when the maximum cycle length

ℓ_{2} = \infty

for local boundary conditions . We point out that the book provides a detailed account for transport equations in biology where the mathematical analysis of various kinds of such equations was derived.…”

Section: Introductionmentioning

confidence: 99%

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

Ariza-Ruiz

Garcia-Falset

Latrach

2017

Math Methods in App Sciences

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The present article deals with existence and uniqueness results for a nonlinear evolution initial-boundary value problem, which originates in an age-structured cell population model introduced by Lebowitz and Rubinow (1974) describing the growth of a cell population. Cells of this population are distinguished by age a and cycle length l. In our framework, daughter and mother cells are related by a general reproduction rule that covers all known biological ones. In this paper, the cycle length l is allowed to be infinite. This hypothesis introduces some mathematical difficulties. We consider both local and nonlocal boundary conditions.

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“…We note that a stationary version of problem was discussed in the space L 1 when the maximum cycle length

ℓ_{2} = \infty

Section: Introductionmentioning

confidence: 99%

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

Ariza-Ruiz

Garcia-Falset

Latrach

2017

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

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Existence results for some nonlocal partial integrodifferential equations without compactness or equicontinuity

Ezzinbi

Ghnimi

Taoudi

2019

J. Fixed Point Theory Appl.

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Fixed point methods and accretivity for perturbed nonlinear equations in Banach spaces

Garcia-Falset

Muñiz-Pérez

2020

Journal of Mathematical Analysis and Applications

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On the solutions for a nonlinear boundary value problem modeling a proliferating cell population with inherited cycle length

Cited by 3 publications

References 21 publications

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

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

Existence results for some nonlocal partial integrodifferential equations without compactness or equicontinuity

Fixed point methods and accretivity for perturbed nonlinear equations in Banach spaces

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