Exact non-classical symmetry solutions of Arrhenius reaction-diffusion

P. Broadbridge, B. H. Bradshaw-Hajek, D. Triadis

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


Exact solutions for nonlinear Arrhenius reaction- diffusion are constructed in n-dimensions. A single relationship between nonlinear diffusivity and the nonlinear reaction term leads to a non-classical Lie symmetry whose invariant solutions have a heat flux that is exponential in time (either growth or decay), and satisfying a linear Helmholtz equation in space. This construction also extends to heterogeneous diffusion wherein the nonlinear diffusivity factorizes to the product of a function of temperature and a function of position. Example solutions are given with applications to heat conduction in conjunction with either exothermic or endothermic reactions, and to soil-water flow in conjunction with water extraction by a web of plant roots.

Original languageEnglish
Article number20150580
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2184
Publication statusPublished - Dec 8 2015

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)


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