Transition from pushed-to-pulled fronts in piecewise linear reaction–diffusion systems

The propagation of a reaction front is considered in the framework of the Seki–Lindenberg reaction–subdiffusion model, which is appropriate in the case of a diffusion-limited reaction. Typically, this kind of problem is solved using approximate approaches or numerical methods. We apply a model piecewise linear reaction function, which allows for exact analytical solutions. For a front between two stable homogeneous states, a unique value of the front velocity is found. In the case of fronts between a stable and an unstable state, a family of traveling wave solutions is revealed. The conditions for the existence of a special ‘pushed’ front are considered. The influence of advection on the front velocity is also analyzed.

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Variational principles and the effect of a cutoff on population pattern size

Méndez

Horsthemke

Casas-Vázquez

et al. 2007

Eur. Phys. J. Spec. Top.

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Transition from pushed-to-pulled fronts in piecewise linear reaction–diffusion systems

Cited by 3 publications

References 26 publications

Exact solutions in front propagation problems with superdiffusion

Exact solutions in front propagation problems with superdiffusion

An exactly solvable model of subdiffusion–reaction front propagation

Variational principles and the effect of a cutoff on population pattern size

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