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    Pointwise asymptotic behavior of modulated periodic reaction-diffusion waves

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    By working with the periodic resolvent kernel and Bloch-decomposition, we establish pointwise bounds for the Green function of the linearized equation associated with spatially periodic traveling waves of a system of reaction diffusion equations.With our linearized estimates together with a nonlinear iteration scheme developed by Johnson-Zumbrun, we obtain LpL^p- behavior(p1p \geq 1) of a nonlinear solution to a perturbation equation of a reaction-diffusion equation with respect to initial data in L1H1L^1 \cap H^1 recovering and slightly sharpening results obtained by Schneider using weighted energy and renormalization techniques. We obtain also pointwise nonlinear estimates with respect to two different initial perturbations u0E0ex2/M|u_0|\leq E_0e^{-|x|^2/M} and u0E0(1+x)3/2|u_0| \leq E_0(1+|x|)^{-3/2}, respectively, E0>0E_0>0 sufficiently small and M>1M>1 sufficiently large, showing that behavior is that of a heat kernel. These pointwise bounds have not been obtained elsewhere, and do not appear to be accessible by previous techniques

    Margaret Cavendish's mythopoetics: by way of introduction

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