### Abstract

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 language | English |
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Article number | 20150580 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 471 |

Issue number | 2184 |

DOIs | |

Publication status | Published - Dec 8 2015 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*,

*471*(2184), [20150580]. https://doi.org/10.1098/rspa.2015.0580

**Exact non-classical symmetry solutions of Arrhenius reaction-diffusion.** / Broadbridge, P.; Bradshaw-Hajek, B. H.; Triadis, D.

Research output: Contribution to journal › Article

*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*, vol. 471, no. 2184, 20150580. https://doi.org/10.1098/rspa.2015.0580

}

TY - JOUR

T1 - Exact non-classical symmetry solutions of Arrhenius reaction-diffusion

AU - Broadbridge, P.

AU - Bradshaw-Hajek, B. H.

AU - Triadis, D.

PY - 2015/12/8

Y1 - 2015/12/8

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84956867066&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84956867066&partnerID=8YFLogxK

U2 - 10.1098/rspa.2015.0580

DO - 10.1098/rspa.2015.0580

M3 - Article

AN - SCOPUS:84956867066

VL - 471

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 0080-4630

IS - 2184

M1 - 20150580

ER -