Q_(p)上分形多孔介质的流体动力学模型

Modeling fluid’s dynamics in fractal porous media on Q_(p)

利用p-adic域中的同胚映射,将在超距空间上多孔介质的流体动力学模型推广至分形集,运用苏维宜定义的拟微分算子T^(α),研究了一类满足初始条件的液体滴在分形多孔介质上流体动力学的反应扩散拟微分方程,得到了该方程的定解,并进一步讨论了该定解的敛散性。

By using the homeomorphism mapping on p-adic field,we extend the fluid's dynamical model in porous media on ultrametric spaces to the fractal sets.We consider a class of reaction-diffusion pseudo-differential equations representing the fluid's dynamics of liquid drop through the fractal porous media by using the pseudo-differential operator T^(α) defined by SU Weiyi.The exact solutions are obtained and convergence of the solutions is further discussed.