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Exact Solutions of Linear Reaction-Diffusion Processes on a Uniformly Growing Domain: Criteria for Successful Colonization

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  • Matthew J Simpson

Abstract

Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction—diffusion process on 0

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  • Matthew J Simpson, 2015. "Exact Solutions of Linear Reaction-Diffusion Processes on a Uniformly Growing Domain: Criteria for Successful Colonization," PLOS ONE, Public Library of Science, vol. 10(2), pages 1-11, February.
    • Handle: RePEc:plo:pone00:0117949
    DOI: 10.1371/journal.pone.0117949
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    References listed on IDEAS

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    1. Rebecca H Chisholm & Barry D Hughes & Kerry A Landman, 2010. "Building a Morphogen Gradient without Diffusion in a Growing Tissue," PLOS ONE, Public Library of Science, vol. 5(9), pages 1-9, September.
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    Cited by:

    1. Cristian Ghiu & Constantin Udriste, 2022. "Solutions for Multitime Reaction–Diffusion PDE," Mathematics, MDPI, vol. 10(19), pages 1-12, October.

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