Summary
Free boundary problems associated with biological tissue growing under conditions of nutrient limitation are formulated. Analysis by linear-stability methods, clarifying the models’ stability properties, is then described.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Drasdo, D.: Buckling instabilities of one-layered growing tissues. Phys. Rev. Lett., 84, 4244–4247 (2000).
Franks, S.J.: Mathematical modelling of tumour growth and stability. Ph.D. Thesis, University of Nottingham (2001).
Franks, S.J., King, J.R.: Interactions between a uniformly proliferating tumour and its surroundings: uniform material properties. Math. Med. Biol., 20, 47–89 (2003).
King, J.R.: Mathematical aspects of semiconductor process modelling. Ph.D. Thesis, University of Oxford (1986).
King, J.R., Franks, S.J.: Mathematical analysis of some multi-dimensional tissue growth models. Euro. J. Appl. Math. 15, 273–295 (2004).
Ward, J.P., King, J.R.: Mathematical modelling of avascular-tumour growth. J. Math. Appl. Med. Biol. 14, 39–69 (1997).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 springer
About this chapter
Cite this chapter
King, J., Franks, S. (2007). Stability Properties of Some Tissue-Growth Models. In: Deutsch, A., Brusch, L., Byrne, H., Vries, G.d., Herzel, H. (eds) Mathematical Modeling of Biological Systems, Volume I. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4558-8_15
Download citation
DOI: https://doi.org/10.1007/978-0-8176-4558-8_15
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4557-1
Online ISBN: 978-0-8176-4558-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)