Citation: Jacek Banasiak, Aleksandra Falkiewicz. A singular limit for an age structured mutation problem[J]. Mathematical Biosciences and Engineering, 2017, 14(1): 17-30. doi: 10.3934/mbe.2017002
[1] | [ H. Amann and J. Escher, Analysis II Birkhäuser, Basel 2008. |
[2] | [ W. Arendt, Resolvent positive operators, Proc. Lond. Math. Soc., 54 (1987): 321-349. |
[3] | [ J. Banasiak,L. Arlotti, null, Positive Perturbations of Semigroups with Applications, Springer Verlag, London, 2006. |
[4] | [ J. Banasiak and A. Falkiewicz, Some transport and diffusion processes on networks and their graph realizability Appl. Math. Lett. ,45 (2015), 25-30 |
[5] | [ J. Banasiak, A. Falkiewicz and P. Namayanja, Semigroup approach to diffusion and transport problems on networks Semigroup Forum. [DOI 10.1007/s00233-015-9730-4] |
[6] | [ J. Banasiak,A. Falkiewicz,P. Namayanja, Asymptotic state lumping in transport and diffusion problems on networks with applications to population problems, Math. Models Methods Appl. Sci., 26 (2016): 215-247. |
[7] | [ J. Banasiak and M. Lachowicz, Methods of Small Parameter in Mathematical Biology Birkhäuser/Springer, Cham, 2014. |
[8] | [ J. Banasiak,M. Moszyński, Dynamics of birth-and-death processes with proliferation -stability and chaos, Discrete Contin. Dyn. Syst., 29 (2011): 67-79. |
[9] | [ A. Bobrowski, null, Functional Analysis for Probability and Stochastic Processes, Cambridge University Press, Cambridge, 2005. |
[10] | [ A. Bobrowski, null, Convergence of One-parameter Operator Semigroups. In Models of Mathematical Biology and Elsewhere, Cambridge University Press, Cambridge, 2016. |
[11] | [ A. Bobrowski, On Hille-type approximation of degenerate semigroups of operators, Linear Algebra and its Applications, 511 (2016): 31-53. |
[12] | [ A. Bobrowski,M. Kimmel, Asymptotic behaviour of an operator exponential related to branching random walk models of DNA repeats, J. Biol. Systems, 7 (1999): 33-43. |
[13] | [ B. Dorn, Semigroups for flows in infinite networks, Semigroup Forum, 76 (2008): 341-356. |
[14] | [ K. J. Engel,R. Nagel, null, One-Parameter Semigroups for Linear Evolution Equations, Springer Verlag, New York, 1999. |
[15] | [ M. Kimmel,D. N. Stivers, Time-continuous branching walk models of unstable gene amplification, Bull. Math. Biol., 50 (1994): 337-357. |
[16] | [ M. Kimmel,A. Świerniak,A. Polański, Infinite-dimensional model of evolution of drug resistance of cancer cells, J. Math. Systems Estimation Control, 8 (1998): 1-16. |
[17] | [ M. Kramar,E. Sikolya, Spectral properties and asymptotic periodicity of flows in networks, Math. Z., 249 (2005): 139-162. |
[18] | [ J. L. Lebowitz,S. I. Rubinov, A theory for the age and generation time distribution of a microbial population, J. Theor. Biol., 1 (1974): 17-36. |
[19] | [ C. D. Meyer, Matrix Analysis and Applied Linear Algebra SIAM, Philadelphia, 2000. |
[20] | [ P. Namayanja, Transport on Network Structures Ph. D thesis, UKZN, 2012. |
[21] | [ M. Rotenberg, Transport theory for growing cell population, J. Theor. Biol., 103 (1983): 181-199. |
[22] | [ A. Świerniak, A. Polański and M. Kimmel, Control problems arising in chemotherapy under evolving drug resistance, Preprints of the 13th World Congress of IFAC 1996, Volume B, 411-416. |
[23] | [ H. T. K. Tse, W. McConnell Weaver and D. Di Carlo, Increased asymmetric and multi-daughter cell division in mechanically confined microenvironments PLoS ONE, 7 (2012), e38986. |