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Efendiyev, M.A. ; van Brunt, B.* ; Wake, G.C.* ; Zaidi, A.A.*

A functional partial differential equation arising in a cell growth model with dispersion.

Math. Meth. Appl. Sci., DOI: 10.1002/mma.4684 (2017)
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In this paper we solve an initial-boundary value problem that involves a pde with a nonlocal term. The problem comes from a cell division model where the growth is assumed to be stochastic. The deterministic version of this problem yields a first-order pde; the stochastic version yields a second-order parabolic pde. There are no general methods for solving such problems even for the simplest cases owing to the nonlocal term. Although a solution method was devised for the simplest version of the first-order case, the analysis does not readily extend to the second-order case. We develop a method for solving the second-order case and obtain the exact solution in a form that allows us to study the long time asymptotic behaviour of solutions and the impact of the dispersion term. We establish the existence of a large time attracting solution towards which solutions converge exponentially in time. The dispersion term does not appear in the exponential rate of convergence.
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Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
Schlagwörter Cell Division ; Functional Differential Equation ; Parabolic Partial Differential Equation
ISSN (print) / ISBN 0170-4214
e-ISSN 1099-1476
Verlag Wiley