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Asymmetric cell division with stochastic growth rate. Dedicated to the memory of the late Spartak Agamirzayev
Author(s) -
Efendiev Messoud,
Brunt Bruce,
Zaidi Ali A.,
Shah Touqeer H.
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5269
Subject(s) - mathematics , division (mathematics) , separable space , partial differential equation , mathematical analysis , boundary value problem , cell division , parabolic partial differential equation , population , convergence (economics) , cell , arithmetic , genetics , demography , sociology , biology , economics , economic growth
A cell growth model for a size‐structured cell population with a stochastic growth rate for size and division into two daughter cells of unequal size is studied in this paper. The model entails an initial boundary value problem that involves a second‐order parabolic partial differential equation with two nonlocal terms, the presence of which is a consequence of asymmetry in the cell division. The solution techniques for solving such problems are rare due to the nonlocal terms. In this paper, we solve the initial boundary value problem for arbitrary initial distributions. We obtain a separable solution, as well as the general solution to the partial differential equation, and show that the solutions converge to the separable solution for large time. As in the symmetric division case, the dispersion term does not affect the rate of convergence to the separable solution.