Speed-up of combustion fronts in shear flows
Speed-up of combustion fronts in shear flows
复制标题
剪切流中燃烧前沿的加速
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Andrej Zlatoš
中科院分区：
文献类型：
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作者：
F. Hamel;Andrej Zlatoš
本文研究了具有周期边界条件的无限长圆柱体中反应-扩散-平流波前的加速问题。平流是一个剪切流与一个大的振幅和反应是非负的，与正或零点火温度。当流动振幅趋于无穷大时，行进前沿的唯一或最小速度被证明在流动振幅中是渐近线性的，解决了Berestycki的一个公开问题（凝聚物质和反应流中的非线性偏微分方程，Kluwer，Doordrecht，2003）。渐近增长率的特点是明确的唯一或最小速度的旅行前的限制退化问题，和收敛的正规旅行前退化的证明了正点火温度下的一个额外的Hörmander型条件的流动。
This paper is concerned with the analysis of speed-up of reaction-diffusion-advection traveling fronts in infinite cylinders with periodic boundary conditions. The advection is a shear flow with a large amplitude and the reaction is nonnegative, with either positive or zero ignition temperature. The unique or minimal speeds of the traveling fronts are proved to be asymptotically linear in the flow amplitude as the latter goes to infinity, solving an open problem from Berestycki (Nonlinear PDEs in condensed matter and reactive flows, Kluwer, Doordrecht, 2003). The asymptotic growth rate is characterized explicitly as the unique or minimal speed of traveling fronts for a limiting degenerate problem, and the convergence of the regular traveling fronts to the degenerate ones is proved for positive ignition temperatures under an additional Hörmander-type condition on the flow.