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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Group Classification and Solutions of a Mathematical Model from Tumour Biology

Discontinuity, Nonlinearity, and Complexity 10(4) (2021) 605--615 | 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, SE-371 79 Karlskrona, Sweden Ufa State Aviation Technical University,

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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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