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A group analysis via weak equivalence transformations for a model of tumour encapsulation. (English) Zbl 1045.92022
Summary: A symmetry reduction of a PDEs system, describing the expansive growth of a benign tumour, is obtained via a group analysis approach. The presence of three arbitrary functions in the model suggests the use of Lie symmetries by using weak equivalence transformations. An invariant classification is given which allows us to reduce the initial PDEs system to an ODEs system. Numerical simulations show a realistic enough description of the physical process.

MSC:
92C50Medical applications of mathematical biology
35K55Nonlinear parabolic equations
35A30Geometric theory for PDE, characteristics, transformations
35Q80Applications of PDE in areas other than physics (MSC2000)
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