Propagating Waves and Target Patterns in Chemical Systems.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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A class of models for target patterns concentric circular waves emanating from a point called the leading center is constructed in the context of singularly perturbed reaction-diffusion systems of partial differential equations. First, the theory of wave fronts is detailed for scalar equations and systems of equations. A scaling method reduces complex waves to the consideration of a group of simple wave phenomena. It is shown that expanding wave fronts can be generated spontaneously at a point. This process, together with the laws of their subsequent motion, reduces the problem to an ordinary differential initial value problem, whose solution is required to have certain properties. A discussion is given of the connection between these results and experimental observations. Author
- Physical Chemistry
- Numerical Mathematics