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A generalisation of reaction diffusion systems and their travelling solutionsto cases when the productive part of the reaction happens only on a surface inspace or on a line on plane but the degradation and the diffusion happen inbulk are important for modelling various biological processes. These includeproblems of invasive species propagation along boundaries of ecozones, problemsof gene spread in such situations, morphogenesis in cavities, intracellularreaction etc. Piecewise linear approximations of reaction terms inreaction-diffusion systems often result in exact solutions of propagation frontproblems. This article presents an exact travelling solution for areaction-diffusion system with a piecewise constant production restricted to acodimension-1 subset. The solution is monotone, propagates with the uniqueconstant velocity, and connects the trivial solution to a nontrivialnonhomogeneous stationary solution of the problem. The properties of thesolution closely parallel the properties of monotone travelling solutions inclassical bistable reaction-diffusion systems.

Exact travelling solution for a reaction-diffusion system with a piecewise constant production supported by a codimension-1 subspace