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Propagation speeds of disturbances are bounded for a class of reaction–diffusion systems

It is shown in a rigorous way that propagation speeds of disturbances are bounded for a class of reaction–diffusion systems. It turns out that solutions for various initial states are confined by traveling waves. A new technique is developed for the construction of the comparison functions. The technique is based on the operator-splitting methodology, which is known as a numerical computation method. By using an exact solution of the Fisher equation we can make a simple proof. The upper bounds of the speeds are given explicitly in terms of the diffusion constants and the Lipschitz norms of the reaction terms.