标题： 对异常扩散的对流的渐近行为 显示英文标题

标题： Asymptotic behaviour for convection with anomalous diffusion

摘要： 我们研究了对流在Darcy多孔材料中的完全非线性模型，其中扩散为异常类型，如Barletta最近提出的那样。 完全非线性模型被分析，但我们允许变量重力或渗透对流效应，这导致空间依赖的系数。 这种空间依赖性通常即使在线性化情况下也需要数值解。 在本工作中，我们证明无论瑞利数的大小如何，对于超扩散情况，扰动解将随时间呈指数衰减。 此外，我们建立了类似的结果，用于双分散多孔介质中的对流，其中同时存在宏观和微观孔隙度效应。 此外，我们还证明了热盐对流中类似的结论。 显示英文摘要

摘要： We investigate the fully nonlinear model for convection in a Darcy porous material where the diffusion is of anomalous type as recently proposed by Barletta. The fully nonlinear model is analysed but we allow for variable gravity or penetrative convection effects which result in spatially dependent coefficients. This spatial dependence usually requires numerical solution even in the linearized case. In this work we demonstrate that regardless of the size of the Rayleigh number the perturbation solution will decay exponentially in time for the superdiffusion case. In addition we establish a similar result for convection in a bidisperse porous medium where both macro and micro porosity effects are present. Moreover, we demonstrate a similar result for thermosolutal convection.