arXiv subjects

B. H. Bradshaw-Hajek

Publications and source records attributed to B. H. Bradshaw-Hajek.

2 recordsLinked to original sources

arXiv2026

Instability of solutions in a degenerate reaction diffusion equation

We study the spectral stability of travelling and stationary front and pulse solutions in a class of degenerate reaction-diffusion systems. We characterise the essential spectrum of the linearised operator in full generality and identify conditions under which it lies entirely in the left-half plane. For a number of special cases we obtain analytical results, including explicit Evans functions, and complete spectral descriptions for certain stationary waves. In regimes where analytical methods are not available, we compute the point spectrum numerically using a Riccati-Evans function approach. Our results show that stable travelling fronts can occur, while travelling pulses are typically unstable.

math.AP↗

arXiv2015

Exact nonclassical symmetry solutions of Arrhenius reaction-diffusion

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 nonclassical 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 extends also to heterogeneous diffusion wherein the nonlinear diffusivity factorises 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.

math.AP↗