论文标题
在多孔培养基流动的背景下，限制晶体溶解和降水模型以及不稳定的Stokes方程的分析
Limiting analysis of a crystal dissolution and precipitation model coupled with the unsteady stokes equations in the context of porous media flow
论文作者
论文摘要
我们研究了流动化学物种的扩散反应 - 参与模型，以及微尺度多孔培养基中固定物种的溶解和沉淀。这导致了孔隙空间中半线性抛物线偏微分方程的系统，并在固体矩阵的晶界面上与非线性普通微分方程相结合。孔隙空间内的流体流由不稳定的Stokes方程式给出。这项工作的新颖性是通过解决非线性项，单调多值溶解率项，依赖于空间依赖的非相同的非相同扩散系数和非线性降水（反应）项来对系统进行迭代限制分析。我们还确定了耦合系统的独特积极全球弱解决方案的存在。除此之外，为了进行升级，我们介绍了扩展运算符的修改版本。最后，我们通过表明高尺度模型允许独特的解决方案来结束论文。
We study the diffusion-reaction-advection model for mobile chemical species together with the dissolution and precipitation of immobile species in a porous medium at the micro-scale. This leads to a system of semilinear parabolic partial differential equations in the pore space coupled with a nonlinear ordinary differential equation at the grain boundary of the solid matrices. The fluid flow within the pore space is given by unsteady Stokes equation. The novelty of this work is to do the iterative limit analysis of the system by tackling the nonlinear terms, monotone multi-valued dissolution rate term, space-dependent non-identical diffusion coefficients and nonlinear precipitation (reaction) term. We also establish the existence of a unique positive global weak solution for the coupled system. In addition to that, for upscaling we introduce a modified version of the extension operator. Finally, we conclude the paper by showing that the upscaled model admits a unique solution.
