Publication: Lie point symmetries for generalised Fisher's equations describing tumour dynamics
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Date
2021-04-12
Authors
Chulián, Salvador
Martinez-Rubio, Álvaro
Gandarias, María Luz
Rosa, María
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AIMS Press
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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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MeSH Terms
Medical Subject Headings::Organisms::Eukaryota::Animals::Chordata::Vertebrates::Mammals::Primates::Haplorhini::Catarrhini::Hominidae::Humans
Medical Subject Headings::Disciplines and Occupations::Natural Science Disciplines::Mathematics
Medical Subject Headings::Diseases::Neoplasms
Medical Subject Headings::Phenomena and Processes::Biological Phenomena
Medical Subject Headings::Disciplines and Occupations::Natural Science Disciplines::Physics
Medical Subject Headings::Analytical, Diagnostic and Therapeutic Techniques and Equipment::Investigative Techniques::Models, Theoretical::Nonlinear Dynamics
Medical Subject Headings::Analytical, Diagnostic and Therapeutic Techniques and Equipment::Investigative Techniques::Models, Theoretical::Models, Biological::Models, Genetic
Medical Subject Headings::Disciplines and Occupations::Natural Science Disciplines::Mathematics
Medical Subject Headings::Diseases::Neoplasms
Medical Subject Headings::Phenomena and Processes::Biological Phenomena
Medical Subject Headings::Disciplines and Occupations::Natural Science Disciplines::Physics
Medical Subject Headings::Analytical, Diagnostic and Therapeutic Techniques and Equipment::Investigative Techniques::Models, Theoretical::Nonlinear Dynamics
Medical Subject Headings::Analytical, Diagnostic and Therapeutic Techniques and Equipment::Investigative Techniques::Models, Theoretical::Models, Biological::Models, Genetic
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Keywords
Lie symmetries, Fisher’s equations, Generalized Fisher’s equations, Tumor dynamics, Partial differential equations, Neoplasias, Matemática, Dinámicas no lineales, Fenómenos biológicos
Citation
Chulián S, Martinez-Rubio Á, Gandarias ML, Rosa M. Lie point symmetries for generalised Fisher's equations describing tumour dynamics. Math Biosci Eng. 2021 Apr 12;18(4):3291-3312