The discrete fragmentation equation: Semigroups, compactness and asynchronous exponential growth

Jacek Banasiak;  ; Wilson Lamb;

doi:10.3934/krm.2012.5.223

The discrete fragmentation equation: Semigroups, compactness and asynchronous exponential growth

Kinetic and Related Models ◽

10.3934/krm.2012.5.223 ◽

2012 ◽

Vol 5 (2) ◽

pp. 223-236 ◽

Cited By ~ 9

Author(s):

Jacek Banasiak ◽

◽

Wilson Lamb ◽

Keyword(s):

Exponential Growth ◽

Asynchronous Exponential Growth ◽

Fragmentation Equation

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Asynchronous exponential growth of the growth-fragmentation equation with unbounded fragmentation rate

Journal of Evolution Equations ◽

10.1007/s00028-019-00526-4 ◽

2019 ◽

Vol 20 (2) ◽

pp. 375-401 ◽

Cited By ~ 1

Author(s):

Étienne Bernard ◽

Pierre Gabriel

Keyword(s):

Exponential Growth ◽

Fragmentation Rate ◽

Asynchronous Exponential Growth ◽

Fragmentation Equation

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Asynchronous Exponential Growth in Transition Probability Models of the Cell Cycle

SIAM Journal on Mathematical Analysis ◽

10.1137/0518068 ◽

1987 ◽

Vol 18 (4) ◽

pp. 897-908 ◽

Cited By ~ 9

Author(s):

G. F. Webb ◽

A. Grabosch

Keyword(s):

Cell Cycle ◽

Exponential Growth ◽

Transition Probability ◽

Probability Models ◽

Asynchronous Exponential Growth

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Positive perturbation of operator semigroups: growth bounds, essential compactness and asynchronous exponential growth

Discrete and Continuous Dynamical Systems ◽

10.3934/dcds.1998.4.735 ◽

1998 ◽

Vol 4 (4) ◽

pp. 735-764 ◽

Cited By ~ 20

Author(s):

Horst R. Thieme ◽

Keyword(s):

Exponential Growth ◽

Operator Semigroups ◽

Asynchronous Exponential Growth

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Asynchronous exponential growth in an age structured population of proliferating and quiescent cells

Mathematical Biosciences ◽

10.1016/s0025-5564(01)00097-9 ◽

2002 ◽

Vol 177-178 ◽

pp. 73-83 ◽

Cited By ~ 33

Author(s):

Janet Dyson ◽

Rosanna Villella-Bressan ◽

G.F. Webb

Keyword(s):

Exponential Growth ◽

Quiescent Cells ◽

Structured Population ◽

Asynchronous Exponential Growth ◽

Age Structured ◽

Age Structured Population

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Necessary and Sufficient Conditions for Asynchronous Exponential Growth in Age Structured Cell Populations with Quiescence

Journal of Mathematical Analysis and Applications ◽

10.1006/jmaa.1997.5654 ◽

1997 ◽

Vol 215 (2) ◽

pp. 499-513 ◽

Cited By ~ 32

Author(s):

O. Arino ◽

E. Sánchez ◽

G.F. Webb

Keyword(s):

Exponential Growth ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Cell Populations ◽

Asynchronous Exponential Growth ◽

Age Structured ◽

Necessary And Sufficient

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Asynchronous exponential growth of semigroups of nonlinear operators

Journal of Mathematical Analysis and Applications ◽

10.1016/0022-247x(92)90218-3 ◽

1992 ◽

Vol 167 (2) ◽

pp. 443-467 ◽

Cited By ~ 20

Author(s):

M Gyllenberg ◽

G.F Webb

Keyword(s):

Exponential Growth ◽

Nonlinear Operators ◽

Asynchronous Exponential Growth

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Asynchronous exponential growth for a two-phase size-structured population model and comparison with the corresponding one-phase model

Journal of Biological Dynamics ◽

10.1080/17513758.2018.1501104 ◽

2018 ◽

Vol 12 (1) ◽

pp. 683-699

Author(s):

Meng Bai ◽

Shihe Xu

Keyword(s):

Exponential Growth ◽

Population Model ◽

Phase Model ◽

Two Phase ◽

Structured Population Model ◽

Structured Population ◽

Phase Size ◽

Asynchronous Exponential Growth

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Asynchronous Exponential Growth in Differential Equations with Homogeneous Nonlinearities

differential equations in Banach spaces ◽

10.1201/9781003072102-17 ◽

2020 ◽

pp. 225-233 ◽

Cited By ~ 1

Author(s):

G.F. Webb

Keyword(s):

Differential Equations ◽

Exponential Growth ◽

Asynchronous Exponential Growth

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An operator-theoretic formulation of asynchronous exponential growth

Transactions of the American Mathematical Society ◽

10.1090/s0002-9947-1987-0902796-7 ◽

1987 ◽

Vol 303 (2) ◽

pp. 751-751 ◽

Cited By ~ 55

Author(s):

G. F. Webb

Keyword(s):

Exponential Growth ◽

Asynchronous Exponential Growth

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Asynchronous exponential growth for an age dependent population equation with delayed birth process

Journal of Evolution Equations ◽

10.1007/s00028-004-0159-6 ◽

2005 ◽

Vol 5 (1) ◽

pp. 61-77 ◽

Cited By ~ 23

Author(s):

Susanna Piazzera ◽

Lorenza Tonetto

Keyword(s):

Exponential Growth ◽

Birth Process ◽

Age Dependent ◽

Asynchronous Exponential Growth ◽

Population Equation

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