|Title||Analytical solutions to nonlinear reaction-diffusion equations in different coordinate systems|
|Presenter||Bronwyn Hajek (University of South Australia)|
|Session||Analysis and Partial Differential Equations|
Nonlinear reaction-diffusion equations are used to describe many different processes in biology and chemistry, for example, population dynamics, cell proliferation, and chemical reactions. In this talk, I'll show how the nonclassical symmetry method can be used to find analytic solutions to nonlinear reaction-diffusion equations. Provided the nonlinear reaction and nonlinear diffusion terms are related in a certain way, there exists a nonclassical symmetry that gives rise to a transformation that will linearise and separate (in time and space) the reaction-diffusion equation, so that analytic solutions may be constructed. The transformation is valid in different coordinate systems (eg Cartesian, polar, spherical) and so may be applied in many situations.
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