The equivalence group and invariant solutions of a tumour growth model. (English) Zbl 1032.92017

Ibragimov, Nail H.; Säfström, Niklas

Commun. Nonlinear Sci. Numer. Simul. 9, No. 1, 61-68 (2004).

Summary: Recently, several mathematical models appeared in the literature for describing spread of malignant tumours. These models are formulated as systems of nonlinear partial differential equations containing, in general, several unknown functions of dependent variables. Determination of these unknown functions (called in group analysis arbitrary elements) is a complicated problem that challenges researchers. Our aim is to calculate the generators of the equivalence group for one of the known models and, using the equivalence generators, specify arbitrary elements, find additional symmetries and calculate group invariant solutions.

MSC:

92C50	Medical applications (general)
54H15	Transformation groups and semigroups (topological aspects)
35Q92	PDEs in connection with biology, chemistry and other natural sciences

Keywords:

Tumour growth; Equivalence group; Symmetries; Invariant solutions

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