On a generalized Fisher equation |
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| Affiliation: | 1. School of Mathematical Sciences, Queensland University of Technology (QUT), Brisbane, Australia;2. Landcare Research, Lincoln, Canterbury, New Zealand;3. Biomathematics Research Centre, University of Canterbury, Christchurch, New Zealand;4. Te Pūnaha Matatini, a New Zealand Centre of Research Excellence, New Zealand;5. Ghrelin Research Group, Translational Research Institute, QUT, 37 Kent St, Woolloongabba, Queensland, Australia;1. School of Mathematical Sciences, Xiamen University, Xiamen 361005, PR China;2. Department of Statistics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong;3. School of Statistics, Huaqiao University, Xiamen 361005, PR China |
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| Abstract: | A generalized non-linear Fisher equation in cylindrical coordinates with radial symmetry is studied from Lie symmetry point of view. In the classical Fisher equation the reaction diffusion term is replaced with a general function to accommodate more equations of this type. Moreover, the diffusivity is assumed to be a function of the dependent variable to account for many real situations. An attempt is made to classify the diffusivity function and exact solutions are obtained in some cases. |
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