1. Lie point symmetries for generalised Fisher's equations describing tumour dynamics
- Author
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Maria Luz Gandarias, Álvaro Martínez-Rubio, Salvador Chulián, María Rosa, and Matemáticas
- Subjects
Work (thermodynamics) ,generalized Fisher’s equations ,Differential equation ,lie symmetries ,02 engineering and technology ,Diffusion ,Neoplasms ,generalized Fisher's equations ,0502 economics and business ,partial differential equations ,QA1-939 ,0202 electrical engineering, electronic engineering, information engineering ,Humans ,Applied mathematics ,Fisher’s equations ,Fisher's equations ,Partial differential equation ,Applied Mathematics ,05 social sciences ,Dynamics (mechanics) ,tumor dynamics ,Ode ,General Medicine ,Computational Mathematics ,generalized fisher's equations ,Modeling and Simulation ,Ordinary differential equation ,Homogeneous space ,020201 artificial intelligence & image processing ,Variety (universal algebra) ,partial di erential equations ,General Agricultural and Biological Sciences ,fisher's equations ,TP248.13-248.65 ,Mathematics ,050203 business & management ,Biotechnology - 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., We would like to acknowledge group FQM-201 from Junta de Andalucia. We also would like to acknowledge Profs. Rita Tracina and Mariano Torrisi from the University of Catania (Italy) and Victor M. Perez Garcia from the University of Castilla-La Mancha (Spain) for discussions. This work was partially supported by the Fundacion Espanola para la Ciencia y la Tecnologia [UCA PR214], the Asociacion Pablo Ugarte (APU, Spain) and Inversion Territorial Integrada de la Provincia de Cadiz [ITI-0038-2019].
- Published
- 2021
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