A model of malignant gliomas throug symmetry reductions

María  Rosa; María S.  Bruzón; M. L.  Gandarias

doi:10.3934/proc.2015.0974

Article Contents

2015, Volume 2015: 974-980. Doi: 10.3934/proc.2015.0974 open access

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A model of malignant gliomas throug symmetry reductions

1.
Dpto. de Matemáticas, Universidad de Cádiz, Polígono del Río San Pedro s/n 11510 Puerto Real, Cádiz

Received: August 31, 2014

Revised: April 30, 2015

Published: October 2015

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Abstract

A glioma is a kind of tumor that starts in the brain or spine. The most common site of gliomas is in the brain. Most of the mathematical models in use for malignant gliomas are based on a simple reaction-diffusion equation: the Fisher equation [3]. A nonlinear wave model describing the fundamental features of these tumors has been introduced in [5], by V.M. Pérez and collaborators. In this work, we study this model from the point of view of the theory of symmetry reductions in partial differential equations. We obtain the classical symmetries admitted by the system, then, we use the transformations groups to reduce the equations to ordinary differential equations. Some exact solutions are derived from the solutions of a simple non-linear ordinary differential equation.

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Mathematics Subject Classification: Primary: 76M60, 92D25; Secondary: 35Q91.

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References

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