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Nonclassical Symmetry Solutions for Non-Autonomous Reaction-Diffusion Equations

School of Information Technology and Mathematical Sciences, University of South Australia, Mawson Lakes, SA 5095, Australia
Symmetry 2019, 11(2), 208; https://doi.org/10.3390/sym11020208
Received: 24 December 2018 / Revised: 4 February 2019 / Accepted: 6 February 2019 / Published: 12 February 2019
(This article belongs to the Special Issue Lie Symmetries at Work in Biology and Medicine)
The behaviour of many systems in chemistry, combustion and biology can be described using nonlinear reaction diffusion equations. Here, we use nonclassical symmetry techniques to analyse a class of nonlinear reaction diffusion equations, where both the diffusion coefficient and the coefficient of the reaction term are spatially dependent. We construct new exact group invariant solutions for several forms of the spatial dependence, and the relevance of some of the solutions to population dynamics modelling is discussed. View Full-Text
Keywords: nonclassical symmetries; Q-conditional symmetries; Lie symmetries; exact solutions; reaction-diffusion equations; spatially-dependent diffusion; population dynamics nonclassical symmetries; Q-conditional symmetries; Lie symmetries; exact solutions; reaction-diffusion equations; spatially-dependent diffusion; population dynamics
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Bradshaw-Hajek, B.H. Nonclassical Symmetry Solutions for Non-Autonomous Reaction-Diffusion Equations. Symmetry 2019, 11, 208.

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