Asymptotic behavior of a nonlinear functional-integral equation of cell kinetics with unequal division

DOI10.1007/BF00275817zbMath0715.92011OpenAlexW1981323421WikidataQ52425906 ScholiaQ52425906MaRDI QIDQ752040

Ovide Arino, Marek Kimmel

Publication date: 1989

Published in: Journal of Mathematical Biology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00275817

zbMATH Keywords

nonnegative solutionscell cycle kineticscell cycle controlcytokinesis of metabolic cell constituentsnonlinear functional-integral equationstable steady stateunequal division of cells

Mathematics Subject Classification ID

Groups and semigroups of linear operators (47D03) Asymptotics of solutions to integral equations (45M05) Physiological, cellular and medical topics (92C99)

Related Items (12)

Two simple models of almost the same population with very different dynamics ⋮ A novel mathematical model of heterogeneous cell proliferation ⋮ Cell cycle length and long‐time behavior of an age‐size model ⋮ A nonlinear structured population model of tumor growth with quiescence ⋮ Semigroup Approaches of Cell Proliferation Models ⋮ A cell cycle model and translation semigroups ⋮ A periodicity result for a nonlinear function integral equation ⋮ Asynchronous exponential growth of semigroups of nonlinear operators ⋮ Oscillations in a molecular structured cell population model ⋮ An abstract neutral functional differential equation arising from a cell population model ⋮ Asymptotic behaviour of nonlinear semigroup describing a model of selective cell growth regulation ⋮ Cell cycle kinetics with supramitotic control, two cell types, and unequal division: A model of transformed embryonic cells

Cites Work

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• On the stable size distribution of populations reproducing by fission into two unequal parts
• Random transitions, size control, and inheritance in cell population dynamics
• Theory of functional differential equations. 2nd ed
• Stability analysis of models of cell production systems
• Asymptotic Analysis of a Cell Cycle Model Based on Unequal Division
• Translation Semigroups and Their Linearizations on Spaces of Integrable Functions

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