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The determination of the speed of travelling fronts of the scalar reactiondiffusion equation has been the subject of much study. Using differentapproaches seemingly disconnected variational principles have been established.The purpose of this work is to show the connection between them. For monostablereaction terms, we prove that a principle established by Hadeler and Rothe in1975 and a second one by Benguria and Depassier in 1996 are logicallyequivalent, that is, either can be derived from the other. Two variationalprinciples, formulated for arbitrary reaction terms, are shown to be related bya suitable change of variables. Finally a variational principle proven formonostable reaction terms is shown to be a formulation of the two previous onesin yet another independent variable.

Equivalence of variational principles to determine the speed of scalar reaction diffusion fronts