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A mathematical model for the spread of morphogens with density dependent chemosensitivity

J H Merkin1,3, D J Needham2 and B D Sleeman1

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Recommended by J A Glazier

A system of reaction–diffusion equations with volume-filling chemosensitivity arising in the modelling of morphogen spread during embryonic growth is considered. Existence and uniqueness of classical solutions to this novel system are established. Qualitative behaviour, including similarity structure of solutions, is developed. The existence of weak solutions in certain situations is established and periodic pulse solutions are obtained numerically. The biological interpretation of the results is discussed.


PACS

02.30.Jr Partial differential equations

87.15.Vv Diffusion

87.17.Ee Growth and division

87.17.Aa Modeling, computer simulation of cell processes

05.60.Cd Classical transport

MSC

35K57 Reaction-diffusion equations

92B05 General biology and biomathematics

35K55 Nonlinear PDE of parabolic type

92Cxx Physiological, cellular and medical topics

Subjects

Mathematical physics

Biological physics

Statistical physics and nonlinear systems

Dates

Issue 6 (November 2005)

Received 29 March 2005

Published 3 October 2005



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