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Positive perturbation of operator semigroups: growth bounds, essential compactness and asynchronous exponential growth
1.  Department of Mathematics, Arizona State University, Tempe, AZ 852871804, United States 
[1] 
Jacek Banasiak, Wilson Lamb. The discrete fragmentation equation: Semigroups, compactness and asynchronous exponential growth. Kinetic and Related Models, 2012, 5 (2) : 223236. doi: 10.3934/krm.2012.5.223 
[2] 
Horst R. Thieme. Remarks on resolvent positive operators and their perturbation. Discrete and Continuous Dynamical Systems, 1998, 4 (1) : 7390. doi: 10.3934/dcds.1998.4.73 
[3] 
Frédérique Billy, Jean Clairambault, Franck Delaunay, Céline Feillet, Natalia Robert. Agestructured cell population model to study the influence of growth factors on cell cycle dynamics. Mathematical Biosciences & Engineering, 2013, 10 (1) : 117. doi: 10.3934/mbe.2013.10.1 
[4] 
P. Magal, H. R. Thieme. Eventual compactness for semiflows generated by nonlinear agestructured models. Communications on Pure and Applied Analysis, 2004, 3 (4) : 695727. doi: 10.3934/cpaa.2004.3.695 
[5] 
Z.R. He, M.S. Wang, Z.E. Ma. Optimal birth control problems for nonlinear agestructured population dynamics. Discrete and Continuous Dynamical Systems  B, 2004, 4 (3) : 589594. doi: 10.3934/dcdsb.2004.4.589 
[6] 
George Avalos. Strong stability of PDE semigroups via a generator resolvent criterion. Discrete and Continuous Dynamical Systems  S, 2008, 1 (2) : 207218. doi: 10.3934/dcdss.2008.1.207 
[7] 
Sebastian Aniţa, AnaMaria Moşsneagu. Optimal harvesting for agestructured population dynamics with sizedependent control. Mathematical Control and Related Fields, 2019, 9 (4) : 607621. doi: 10.3934/mcrf.2019043 
[8] 
Linlin Li, Bedreddine Ainseba. Largetime behavior of matured population in an agestructured model. Discrete and Continuous Dynamical Systems  B, 2021, 26 (5) : 25612580. doi: 10.3934/dcdsb.2020195 
[9] 
Diène Ngom, A. Iggidir, Aboudramane Guiro, Abderrahim Ouahbi. An observer for a nonlinear agestructured model of a harvested fish population. Mathematical Biosciences & Engineering, 2008, 5 (2) : 337354. doi: 10.3934/mbe.2008.5.337 
[10] 
Xianlong Fu, Zhihua Liu, Pierre Magal. Hopf bifurcation in an agestructured population model with two delays. Communications on Pure and Applied Analysis, 2015, 14 (2) : 657676. doi: 10.3934/cpaa.2015.14.657 
[11] 
Mustapha MokhtarKharroubi. On spectral gaps of growthfragmentation semigroups with mass loss or death. Communications on Pure and Applied Analysis, 2022, 21 (4) : 12931327. doi: 10.3934/cpaa.2022019 
[12] 
Mustapha MokhtarKharroubi, Jacek Banasiak. On spectral gaps of growthfragmentation semigroups in higher moment spaces. Kinetic and Related Models, 2022, 15 (2) : 147185. doi: 10.3934/krm.2021050 
[13] 
Jacek Banasiak, Wilson Lamb. Coagulation, fragmentation and growth processes in a size structured population. Discrete and Continuous Dynamical Systems  B, 2009, 11 (3) : 563585. doi: 10.3934/dcdsb.2009.11.563 
[14] 
Atul Narang, Sergei S. Pilyugin. Toward an Integrated Physiological Theory of Microbial Growth: From Subcellular Variables to Population Dynamics. Mathematical Biosciences & Engineering, 2005, 2 (1) : 169206. doi: 10.3934/mbe.2005.2.169 
[15] 
Zhihua Liu, Hui Tang, Pierre Magal. Hopf bifurcation for a spatially and age structured population dynamics model. Discrete and Continuous Dynamical Systems  B, 2015, 20 (6) : 17351757. doi: 10.3934/dcdsb.2015.20.1735 
[16] 
Jacques Henry. For which objective is birth process an optimal feedback in age structured population dynamics?. Discrete and Continuous Dynamical Systems  B, 2007, 8 (1) : 107114. doi: 10.3934/dcdsb.2007.8.107 
[17] 
Tristan Roget. On the longtime behaviour of age and trait structured population dynamics. Discrete and Continuous Dynamical Systems  B, 2019, 24 (6) : 25512576. doi: 10.3934/dcdsb.2018265 
[18] 
Peixuan Weng. Spreading speed and traveling wavefront of an agestructured population diffusing in a 2D lattice strip. Discrete and Continuous Dynamical Systems  B, 2009, 12 (4) : 883904. doi: 10.3934/dcdsb.2009.12.883 
[19] 
Yingli Pan, Ying Su, Junjie Wei. Bistable waves of a recursive system arising from seasonal agestructured population models. Discrete and Continuous Dynamical Systems  B, 2019, 24 (2) : 511528. doi: 10.3934/dcdsb.2018184 
[20] 
Guangrui Li, Ming Mei, Yau Shu Wong. Nonlinear stability of traveling wavefronts in an agestructured reactiondiffusion population model. Mathematical Biosciences & Engineering, 2008, 5 (1) : 85100. doi: 10.3934/mbe.2008.5.85 
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