Discontinuity, Nonlinearity, and Complexity
Group Classification and Solutions of a Mathematical Model from Tumour Biology
Discontinuity, Nonlinearity, and Complexity 10(4) (2021) 605615  DOI:10.5890/DNC.2021.12.002
N.H. Ibragimov$^1$, R.Tracina$^2$, E.D. Avdonina$^3$
$^1$ Research Centre ALGA: Advances in Lie Group Analysis, Department of Mathematics and Natural Sciences,
Blekinge Institute of Technology,
SE371 79 Karlskrona, Sweden
Ufa State Aviation Technical University,
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Abstract
We are interested in symmetries of a mathematical model of a malignant tumour dynamics due to haptotaxis.
The model is formulated as a system of two nonlinear partial
differential equations with two independent variables and contains
two unknown functions of the dependent variables. When the unknown
functions are arbitrary, the model has only two symmetries.
These symmetries allow to investigate only travelling wave solutions. The aim of the present paper is to
make the group classification of the mathematical model under
consideration and find the cases when the model has additional
symmetries and hence additional group invariant solutions.
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