3D dynamic Green’s functions in a multilayered poroelastic half-space

The complete 3D dynamic Green’s functions in the multilayered poroelastic media are presented in this study. A method of potentials in cylindrical coordinate system is applied first to decouple the Biot’s wave equations into four scalar Helmholtz equations, and then, general solutions to 3D wave propagation problems are obtained. After that, a three vector base and the propagator matrix method are introduced to treat 3D wave propagation problems in the stratified poroelastic half-space disturbed by buried sources. It is known that the original propagator algorithm has the loss-of-precision problem when the waves become evanescent. At present, an orthogonalization procedure is inserted into the matrix propagation loop to avoid the numerical difficulty of the original propagator algorithm. At last, the validity of the present approach for accurate and efficient calculating 3D dynamic Green’s functions of a multilayered poroelastic half-space is confirmed by comparing the numerical results with the known exact analytical solutions of a uniform poroelastic half-space.     

基于TOPSIS的属性关联直觉模糊多属性决策方法

针对属性值为直觉模糊数,已知部分属性偏好关系及属性交互类型的属性关联多属性决策问题给出决策方法.首先定义方案到正(负)理想方案的距离及各方案与正理想方案相对贴近度.然后以极大化各方案与相对贴近度为目标建立优化模型,确定出属性集的模糊测度.进而基于直觉模糊Choquet积分算子计算各方案的直觉模糊综合评价值,再根据直觉模糊数的得分值及精确度得到方案的排序.最后通过实例验证了方法的有效可行性.     

Vertical vibration of a circular stamp on an elastic-porous half-space with saturation fluid

A specific problem concerning the vertical vibrating response of a composite layer (elastic-porous and saturation fluid) under rigid circular stamp is studied. The motion of the medium is governed byBiot’s dynamic potential equations and the problem is solved by the method of Fourier-Bessel transformation. Formulae are obtained for the vertical displacement of the rigid phase. Graphs are presented for the amplitude of vibration.     

Unique solvability of a linear problem with perturbed periodic boundary values

We investigate the problem with perturbed periodic boundary values

基于方案偏好值的属性关联区间多属性决策

针对属性值为区间数,属性权重完全未知,但给出方案的主观偏好值,部分属性偏好关系以及属性交互类型的属性关联多属性决策问题给出决策方法.首先建立期望值目标规划模型,确定出属性集的M(o|¨)bius表达式以及属性权重,然后利用扩展的区间Choquet积分算子对决策信息进行集结,计算出各方案的区间模糊综合评价值,再利用比较区间数的期望值方法,从而得到方案的最终排序.最后给出了分析实例以说明所提出方法的有效可行性.     

On Moisil-Theodoresko system in a complex form

A $ℂ$-linear problem is considered for the Moisil-Theodorescu system written in a complex form. The Fredholm theorem for this problem is proved, and the index formula obtained.     

某些带变换的边值问题和奇异积分方程

本文主要考虑某些带变换的奇异积分方程。尽管用经典的正则化方法可以求解，我们还是给出一种新的分区跳跃方法，使它们化为较简单的可以系统地求解并可迅即讨论的Ｆｒｅｄｈｏｌｍ积分方程。     

Mean value property and a Berezin-type transform on the half-space

Let B be the open unit ball in Rn. Liu (2007) [6] has shown that if then the iterates of a Berezin-type transform of f converge to the Poisson extension of the boundary values of f, as k→∞. In this paper, we extend this to the half-space setting. First, we obtain the mean value property for harmonic functions on the half-space H. Based on this property, we define a Berezin-type transform BH and investigate the limit of the iterates of BH.     

On mistaken papers by Gouzheng Yan et al and related papers,and on a paper by Weibing Wang and Xuxin Yang

The purpose of the present note is to point out mathematical mistakes in some published papers on boundary value problems to prevent usage of mistaken results and methods by mathematicians. Copyright © 2013 John Wiley & Sons, Ltd.     

Constant-Sign Solutions of a System of Fredholm Integral Equations

We consider the following system of Fredholm intergral equations u _i (t)=₀ ¹ g _i (t,s)f _i (s,u ₁(s),u ₂(s),...,u _n (s)) ds, t[0,1], 1in. Criteria are offered for the existence of single, double and multiple solutions of the system that are of constant signs. The generality of the results obtained is illustrated through applications to several well known boundary value problems. We also extend the above system of Fredholm intergral equations to that on the half-line [0,) u _i (t)=₀ g _i (t,s)f _i (s,u ₁(s),u ₂(s),...,u _n (s)) ds, t[0,), 1in and investigate the existence of constant-sign solutions.     

横观各向同性饱和地基上刚性圆板的扭转振动

通过解析方法研究了横观各向同性饱和半空间上刚性圆板在简谐扭转荷载作用下的振动问题．运用Hankel变换求解了横观各向同性饱和土的动力控制方程,结合混合边界条件得出了刚性基础的扭转对偶积分方程,并将对偶积分方程转化为第二类Fredholm积分方程求解了基础的扭转振动问题,同时给出了动力柔度系数,基础的角位移幅值和基底接触剪应力的表达式．通过数值算例研究了地基的各向异性程度对基础扭转振动的影响．     

Regularized Solutions of a Nonlinear Convolution Equation on the Euclidean Group

In this paper we apply Fourier analysis on the two and three dimensional Euclidean motion groups to the solution of a nonlinear convolution equation. First, we review the theory of the irreducible unitary representations of the motion group and discuss the corresponding Fourier transform of functions on the motion group. The main reasons why exact solutions of this convolution equation do not exist in many cases are discussed. Techniques for regularization of the problem and numerical methods for finding approximate solutions are presented. Examples are considered and approximate solutions are found.     

Dynamics of a rotating layer of an ideal electrically conducting incompressible fluid

A system of nonlinear partial differential equations is considered that models perturbations in a layer of an ideal electrically conducting rotating fluid bounded by spatially and temporally varying surfaces with allowance for inertial forces. The system is reduced to a scalar equation. The solvability of initial boundary value problems arising in the theory of waves in conducting rotating fluids can be established by analyzing this equation. Solutions to the scalar equation are constructed that describe small-amplitude wave propagation in an infinite horizontal layer and a long narrow channel.     

A Contact Problem of the Interaction of a Semi-Finite Inclusion with a Plate

A piece wise-homogeneous plane made up of twodifferent materials and reinforced by an elastic unclusion is considered on a semi-finite section where the different materials join. Vertical and horizontal forces are applied to the inclusion which haz a variable thichness and a variable elasticity modulus.Under certain conditions the problem is reduced to integrodifferential equations of third order. The solution is constructed effectively by applying the methods of theory of analytic functions to a boundary value problem of the Carleman type for a strip. Asymptotic estimates of normal contact stress are obtained.     

层状横观各向同性饱和地基上圆板的非轴对称振动

研究了层状横观各向同性饱和地基上弹性圆板的非轴对称振动问题．首先,通过方位角的Fourier变换,将圆柱坐标系下横观各向同性饱和土的三维动力方程转化为一阶常微分方程组,基于径向Hankel变换,建立问题的状态方程,求解状态方程后得到传递矩阵;其次,利用传递矩阵,结合层状饱和地基的边界条件、排水条件及层间接触和连续条件,给出了任意简谐激振力作用下层状横观各向同性饱和地基动力响应的通解;然后,按混合边值问题建立层状饱和地基上弹性圆板非轴对称振动的对偶积分方程,并将对偶积分方程化为易于数值计算的第二类Fredholm积分方程,并给出了算例．     

A multilevel decoupled method for a mixed Stokes/Darcy model

This paper studies decoupled numerical methods for a mixed Stokes/Darcy model for coupling fluid and porous media flows. A two-level algorithm is proposed and analyzed in Mu and Xu (2007) [10]. We generalize the two-level algorithm to a multilevel algorithm in this paper and present numerical analysis on the error estimates for the multilevel algorithm. The multilevel algorithm solves the mixed Stokes/Darcy system by applying efficient legacy code for single model solvers to solve two decoupled Stokes and Darcy subproblems on all the subsequently refined meshes, except for a much smaller global problem only on a very coarse initial mesh. Numerical experiments are conducted for both the two-level and multilevel algorithms to illustrate their effectiveness and efficiency, and validate the related theoretical analysis.     

An exact solution of start-up flow for the fractional generalized Burgers’ fluid in a porous half-space

Modified Darcy’s law for fractional generalized Burgers’ fluid in a porous medium is introduced. The flow near a wall suddenly set in motion for a fractional generalized Burgers’ fluid in a porous half-space is investigated. The velocity of the flow is described by fractional partial differential equations. By using the Fourier sine transform and the fractional Laplace transform, an exact solution of the velocity distribution is obtained. Some previous and classical results can be recovered from our results, such as the velocity solutions of the Stokes’ first problem for viscous Newtonian, second grade, Maxwell, Oldroyd-B or Burgers’ fluids.     

Nonlinear diffusion equations as asymptotic limits of Cahn‐Hilliard systems on unbounded domains via Cauchy's criterion

This paper develops an abstract theory for subdifferential operators to give existence and uniqueness of solutions to the initial‐boundary problem P for the nonlinear diffusion equation in an unbounded domain ( ), written as which represents the porous media, the fast diffusion equations, etc, where β is a single‐valued maximal monotone function on , and T>0. In Kurima and Yokota (J Differential Equations 2017; 263:2024‐2050 and Adv Math Sci Appl 2017; 26:221‐242) existence and uniqueness of solutions for P were directly proved under a growth condition for β even though the Stefan problem was excluded from examples of P . This paper completely removes the growth condition for β by confirming Cauchy's criterion for solutions of the following approximate problem _ε with approximate parameter ε>0: which is called the Cahn‐Hilliard system, even if ( ) is an unbounded domain. Moreover, it can be seen that the Stefan problem excluded from Kurima and Yokota (J Differential Equations 2017; 263:2024‐2050 and Adv Math Sci Appl 2017; 26:221‐242) is covered in the framework of this paper.