Solution methods for advection-diffusion-reaction equations on growing domains and subdomains, with application to modelling skin substitutes
Adams, Matthew P., Mallet, Daniel G., & Pettet, Graeme J. (2012) Solution methods for advection-diffusion-reaction equations on growing domains and subdomains, with application to modelling skin substitutes. In Gu, YuanTong & Saha, Suvash C. (Eds.) Proceedings of 4th International Conference on Computational Methods (ICCM2012), Gold Coast, Qld. (In Press)
Problems involving the solution of advection-diffusion-reaction equations on domains and subdomains whose growth affects and is affected by these equations, commonly arise in developmental biology. Here, a mathematical framework for these situations, together with methods for obtaining spatio-temporal solutions and steady states of models built from this framework, is presented. The framework and methods are applied to a recently published model of epidermal skin substitutes. Despite the use of Eulerian schemes, excellent agreement is obtained between the numerical spatio-temporal, numerical steady state, and analytical solutions of the model.
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|Item Type:||Conference Paper|
|Keywords:||Growing domain, Nonuniform growth, Continuum, Epithelium, Skin substitute|
|Subjects:||Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Biological Mathematics (010202)|
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical Solution of Differential and Integral Equations (010302)
|Divisions:||Current > Schools > School of Chemistry, Physics & Mechanical Engineering|
Current > Institutes > Institute of Health and Biomedical Innovation
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Past > Schools > Mathematical Sciences
|Copyright Owner:||Copyright 2012 please consult the authors|
|Deposited On:||06 Sep 2012 13:20|
|Last Modified:||25 Feb 2013 14:35|
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