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We show that propagation speeds in invasion processes modeled byreaction-diffusion systems are determined by marginal spectral stabilityconditions, as predicted by the marginal stability conjecture. This conjecturewas recently settled in scalar equations; here we give a full proof for themulti-component case. The main new difficulty lies in precisely characterizingdiffusive dynamics in the leading edge of invasion fronts. To overcome this, weintroduce coordinate transformations which allow us to recognize a leadingorder diffusive equation relying only on an assumption of generic marginalpointwise stability. We are then able to use self-similar variables to give adetailed description of diffusive dynamics in the leading edge, which we matchwith a traveling invasion front in the wake. We then establish front selectionby controlling these matching errors in a nonlinear iteration scheme, relyingon sharp estimates on the linearization about the invasion front. We brieflydiscuss applications to parametrically forced amplitude equations, competitiveLotka-Volterra systems, and a tumor growth model.

Front selection in reaction-diffusion systems via diffusive normal forms