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تسجيل مستخدم جديدEquivalence of variational principles to determine the speed of scalar reaction diffusion fronts
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The determination of the speed of travelling fronts of the scalar reaction diffusion equation has been the subject of much study. Using different approaches seemingly disconnected variational principles have been established. The purpose of this work is to show the connection between them. For monostable reaction terms, we prove that a principle established by Hadeler and Rothe in 1975 and a second one by Benguria and Depassier in 1996 are logically equivalent, that is, either can be derived from the other. Two variational principles, formulated for arbitrary reaction terms, are shown to be related by a suitable change of variables. Finally a variational principle proven for monostable reaction terms is shown to be a formulation of the two previous ones in yet another independent variable.
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