Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On the stability of an ellipsoidal tumour

Authors: George Dassios and Vasiliki Christina Panagiotopoulou
Journal: Quart. Appl. Math. 74 (2016), 399-420
MSC (2010): Primary 92B05, 42C10, 33E10, 33E05, 34B60, 34D10, 53Z05, 65L10
Published electronically: June 16, 2016
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Abstract: The ellipsoid represents the sphere of the anisotropic space. It provides the appropriate geometrical model for any direction dependent physical quantity. The growth of a tumour does depend on the available tissue surrounding the tumour, and therefore it represents a physical case which is realistically modelled by ellipsoidal geometry. Such a model has been analysed recently by Dassios et al. (2012). In the present work, we focus on the stability of the growth of an ellipsoidal tumour. It is shown that, in contrast to the highly symmetric spherical case, where stability can possibly be achieved, there are no conditions that secure the stability of an ellipsoidal tumour. Hence, as in many physical cases, the observed instability is a consequence of the lack of symmetry.

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Additional Information

George Dassios
Affiliation: Department of Chemical Engineering, University of Patras and FORTH/ICE-HT, Greece
Email: gdassios@otenet.gr

Vasiliki Christina Panagiotopoulou
Affiliation: Department of Chemical Engineering, University of Patras and FORTH/ICE-HT, Greece
Email: vpanagi@chemeng.upatras.gr

DOI: https://doi.org/10.1090/qam/1423
Received by editor(s): October 3, 2014
Published electronically: June 16, 2016
Article copyright: © Copyright 2016 Brown University

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