不可压缩核废料污染问题的变网格特征有限元法

1 引言 多孔介质中的核废料污染问题是环境保护领域的重要课题。对于不可压缩二维模型,它是地层中迁移型耦合抛物型方程组的初边值问题:     

层状多孔介质中渗流湿峰的不稳定分析

在部分饱和与部分干的层状多孔介质中，建立了一维渗流问题的数学模型．在自然的条件下，证明了一类退化抛物方程弱解的存在唯一性．揭示了一个重要性质，即当下层介质的孔隙比上层更粗时，层状交界面具有隔水作用．这一作用将会在展状交界面不均匀时导致指状湿峰的出现．同时也说明，较粗孔隙的上层具有防止水分蒸发的作用．     

通过非均匀介质流体的渗流问题

本文讨论三维情形的渗流问题.考虑在坝体形状不规则，且介质不均匀的情况下，将渗流现象归结为线性椭圆方程的自由边值问题.应用变分不等方程理论，证明了解的存在和唯一性.     

流过多孔介质的流体研究

研究流过密集的具二次变化渗透性的重叠理想聚合体的流体．流体流由达西定律的布林克曼扩展及连续方程来刻画,通过引入流函数,求出上述方程在适当边界条件下的解析解,并将结果与一些已知的结果进行了比较．     

具非线性边界条件的非牛顿渗流方程弱解的局部存在性

利用能量方法,证明了一类具有Neumann边界条件的非牛顿渗流方程弱解的局部存在性.     

非线性多孔介质流动模型问题的分歧

本文讨论一类多孔介质流动模型非线性边值问题．对这类问题以及广泛的一类算子方程，我们得到了渐近歧点的存在性     

多孔介质中可压缩流体力学方程组经典解的整体存在性与破裂现象

利用拟线性双曲型方程组极值原理,改进了HSIAO Ling和D.Serre得到的关于多孔介质中可压缩流体力学方程组解的存在性结果,给出了其Cauchy问题的一个关于经典解整体存在和破裂的完整结果．这些结果说明强耗散有助于“小”解的光滑性．     

Homogenization of the Equations of Filtration of a Viscous Fluid in Two Porous Media

A homogenized model of filtration of a viscous fluid in two domains with common boundary is deduced on the basis of the method of two-scale convergence. The domains represent an elastic medium with perforated pores. The fluid, filling the pores, is the same in both domains, and the properties of the solid skeleton are distinct.     

双重介质中二维不定常渗流

本文用积分变换和分离变量等方法,求得了弱压缩液体在双重孔隙介质中,二维不定常渗流的Laplace变换空间解.用数值反演的公式研究了,双重介质裂缝储量比ω和介质间传输系数λ对无限导流垂直裂缝井压力动态的影响.     

Study of Three-Dimensional Boundary Value Problems of Fluid Filtration in an Anisotropic Porous Medium

Three-dimensional boundary value problems (the first and second boundary value problems and the conjugation problem) of stationary filtration of fluids in anisotropic (orthotropic) and inhomogeneous porous media are posed and studied. A medium is characterized by a symmetric permeability tensor whose components generally depend on the coordinates of points of the space. A nonsingular affine transformation of coordinates is used and the problems are stated in canonical form, which dramatically simplifies their study. In the case of orthotropic and piecewise orthotropic homogeneous medium, the solution of the problem with canonical boundaries (plane and ellipsoid surfaces) can be obtained in finite form. In the general case, where the orthotropic medium is inhomogeneous and the boundary surfaces are arbitrary and smooth, the problem can be reduced to singular and hypersingular integral equations. The problems are topical, for example, in the practice of fluid (water, oil) recovery from natural anisotropic and inhomogeneous soil strata.