Lie point symmetries for generalised Fisher's equations describing tumour dynamics

Salvador Chulián; Álvaro Martinez-Rubio; María Luz Gandarias; María Rosa; Salvador Chulián; Álvaro Martinez-Rubio; María Luz Gandarias; María Rosa

doi:10.3934/mbe.2021164

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 4: 3291-3312. doi: 10.3934/mbe.2021164

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Lie point symmetries for generalised Fisher's equations describing tumour dynamics

1.
Departamento de Matemáticas, University of Cádiz, Cádiz, Spain; Instituto de Investigación e Innovación Biomédica de Cádiz (INiBICA), University of Cádiz, Cádiz, Spain
2.
Departamento de Matemáticas, University of Cádiz, Cádiz, Spain

Received: 15 February 2021 Accepted: 24 March 2021 Published: 12 April 2021

A huge variety of phenomena are governed by ordinary differential equations (ODEs) and partial differential equations (PDEs). However, there is no general method to solve them. Obtaining solutions for differential equations is one of the greatest problem for both applied mathematics and physics. Multiple integration methods have been developed to the day to solve particular types of differential equations, specially those focused on physical or biological phenomena. In this work, we review several applications of the Lie method to obtain solutions of reaction-diffusion equations describing cell dynamics and tumour invasion.
- lie symmetries,
- Fisher's equations,
- generalized Fisher's equations,
- tumor dynamics,
- partial differential equations
Citation: Salvador Chulián, Álvaro Martinez-Rubio, María Luz Gandarias, María Rosa. Lie point symmetries for generalised Fisher's equations describing tumour dynamics[J]. Mathematical Biosciences and Engineering, 2021, 18(4): 3291-3312. doi: 10.3934/mbe.2021164

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Abstract

A huge variety of phenomena are governed by ordinary differential equations (ODEs) and partial differential equations (PDEs). However, there is no general method to solve them. Obtaining solutions for differential equations is one of the greatest problem for both applied mathematics and physics. Multiple integration methods have been developed to the day to solve particular types of differential equations, specially those focused on physical or biological phenomena. In this work, we review several applications of the Lie method to obtain solutions of reaction-diffusion equations describing cell dynamics and tumour invasion.

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