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Open Access Green möglich sobald Postprint bei der ZB eingereicht worden ist.
A functional partial differential equation arising in a cell growth model with dispersion.
Math. Meth. Appl. Sci., DOI: 10.1002/mma.4684 (2017)
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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1.017
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Publikationstyp
Artikel: Journalartikel
Dokumenttyp
Wissenschaftlicher Artikel
Schlagwörter
Cell Division ; Functional Differential Equation ; Parabolic Partial Differential Equation
Sprache
englisch
Veröffentlichungsjahr
2017
HGF-Berichtsjahr
2017
ISSN (print) / ISBN
0170-4214
e-ISSN
1099-1476
Zeitschrift
Mathematical Methods in the Applied Sciences
Verlag
Wiley
Begutachtungsstatus
Peer reviewed
Institut(e)
Institute of Computational Biology (ICB)
POF Topic(s)
30205 - Bioengineering and Digital Health
Forschungsfeld(er)
Enabling and Novel Technologies
PSP-Element(e)
G-503800-001
DOI
10.1002/mma.4684
Scopus ID
85038260702
Erfassungsdatum
2017-12-27