Pointwise asymptotic behavior of modulated periodic reaction-diffusion waves
Pointwise asymptotic behavior of modulated periodic reaction-diffusion waves
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调制周期反应扩散波的逐点渐近行为
DOI：
10.1016/j.jde.2012.05.014
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
Soyeun Jung
中科院分区：
文献类型：
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作者：
Soyeun Jung
利用周期预解核和Bloch分解，我们建立了反应扩散方程组的空间周期行波线性化方程的绿色函数的逐点界.利用我们的线性化估计和Johnson-Zumbrun提出的非线性迭代格式，我们得到了反应扩散方程的扰动方程的非线性解关于初始数据的Lp-行为（p ≠ 1），恢复和稍微锐化了Schneider利用加权能量和重整化技术得到的结果.我们还得到了关于两个不同初始扰动的逐点非线性估计[公式：见正文]，[公式：见正文]和|u0| E0（1+）|X|）−r，r>2，[公式：见正文]，E0>0足够小，M>1足够大，表明该行为是热核的行为。这些逐点边界尚未在其他地方获得，并且似乎无法通过先前的技术访问。
By working with the periodic resolvent kernel and the 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 Lp-behavior (p⩾1) of a nonlinear solution to a perturbation equation of a reaction–diffusion equation with respect to initial data in L1∩H2recovering 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 [Formula: see text] , [Formula: see text] and |u0|⩽E0(1+|x|)−r, r>2, [Formula: see text] respectively, E0>0 sufficiently small and M>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.