We derive a precise motion law for fronts of solutions to scalarone-dimensional reaction-diffusion equations with equal depth multiple-wells,in the case the second derivative of the potential vanishes at its minimizers.We show that, renormalizing time in an algebraic way, the motion of fronts isgoverned by a simple system of ordinary differential equations of nearestneighbor interaction type. These interactions may be either attractive orrepulsive. Our results are not constrained by the possible occurrence ofcollisions nor splittings. They present substantial differences with theresults obtained in the case the second derivative does not vanish at thewells, a case which has been extensively studied in the literature, and wherefronts have been showed to move at exponentially small speed, with motion lawswhich are not renormalizable.
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