A group analysis via weak equivalence transformations for a model of tumour encapsulation. (English) Zbl 1045.92022

Gambino, G.; Greco, A. M.; Lombardo, M. C.

J. Phys. A, Math. Gen. 37, No. 12, 3835-3846 (2004).

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:

92C50	Medical applications (general)
35K55	Nonlinear parabolic equations
35A30	Geometric theory, characteristics, transformations in context of PDEs
35Q92	PDEs in connection with biology, chemistry and other natural sciences

Keywords:

weak equivalence classifications