Dynamics of curved reaction fronts under a single-equation model

Abstract

Fronts of reaction in certain systems (such as so-called solid flames) are modelled by a high-order nonlinear partial differential equation, which we analyse numerically. Previously, Strunin [IMA J. Appl. Math. 63:163--177, 1999] obtained stable spinning solutions of the equation using the Galerkin method. Here we use a more sophisticated and arguably more powerful method, namely the one-dimensional radial basis function method, to study the equation further. As an initial step, we elaborate the numerical code and tested it by reproducing the spinning regimes for a range of initial conditions. In a new series of experiments, we find a regime where the front is shaped as a pair of kinks spinning in a stable joint formation. The settled character of this regime is demonstrated. References

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