Quenching of reaction by cellular flows
Quenching of reaction by cellular flows
复制标题
通过细胞流猝灭反应
DOI：
10.1007/s00039-006-0554-y
复制
发表时间：
2005
期刊：
影响因子：
--
通讯作者：
L. Ryzhik
中科院分区：
文献类型：
--
作者：
A. Fannjiang;A. Kiselev;L. Ryzhik
摘要：我们考虑细胞流中的反应扩散方程。我们证明了在强流区，有两种可能的情况下，初始数据是compensarily支持和支持的大小是足够大的。如果流动池与反应长度尺度相比较大，则将总是形成传播前沿。对于小的小区大小，将通过足够强的流来淬灭（quenching）任何受干扰的支持的初始数据。我们估计，抑制支持L0的初始数据所需的流量幅度为
$$A > CL_0^4 \ln \left（{L_0 } \right）.$$问题的实质是对流扩散方程解的L∞范数的衰减问题，以及这种衰减率与二维不可压缩流体流动所产生的Hamilton系统的性质之间的关系。
Abstract.We consider a reaction-diffusion equation in a cellular flow. We prove that in the strong flow regime there are two possible scenarios for the initial data that is compactly supported and the size of the support is large enough. If the flow cells are large compared to the reaction length scale, propagating fronts will always form. For small cell size, any finitely supported initial data will be quenched by a sufficiently strong flow. We estimate that the flow amplitude required to quench the initial data of support L0 is
$$A > CL_0^4 \ln \left( {L_0 } \right).$$ The essence of the problem is the question about the decay of the L∞-norm of a solution to the advection-diffusion equation, and the relation between this rate of decay and the properties of the Hamiltonian system generated by the two-dimensional incompressible fluid flow.