Global smooth solution for the modified anisotropic 3D Boussinesq equations with damping

This paper is mainly concerned with the modified anisotropic three-dimensional Boussinesq equations with damping. We first prove the existence and uniqueness of global solution of velocity anisotropic equations. Then we establish the well-posedness of global solution of temperature anisotropic equations.     

The mathematical modeling of the electric field in the media with anisotropic objects

We present a numerical scheme for modeling the electric field in the media with tensor conductivity. This scheme is based on vector finite element method in frequency domain. The numerical computations of the electric field in the anisotropic medium are done. The conductivity of the anisotropic medium is positive defined dense tensor in general case. We consider the electric field from anisotropic layer, inclined anisotropic layer and some anisotropic objects in isotropic half-space.     

Nonlinear anisotropic elliptic equations in with variable exponents and locally integrable data

In this paper, we prove existence and regularity results for weak solutions in the framework of anisotropic Sobolev spaces for a class of nonlinear anisotropic elliptic equations in the whole with variable exponents and locally integrable data. Our approach is based on the anisotropic Sobolev inequality, a smoothness, and compactness results. The functional setting involves Lebesgue–Sobolev spaces with variable exponents. Copyright © 2016 John Wiley & Sons, Ltd.     

New anisotropic models from isotropic solutions

We establish an algorithm that produces a new solution to the Einstein field equations, with an anisotropic matter distribution, from a given seed isotropic solution. The new solution is expressed in terms of integrals of known functions, and the integration can be completed in principle. The applicability of this technique is demonstrated by generating anisotropic isothermal spheres and anisotropic constant density Schwarzschild spheres. Both of these solutions are expressed in closed form in terms of elementary functions, and this facilitates physical analysis. Copyright © 2005 John Wiley & Sons, Ltd.     

The anisotropic integrability regularity criterion to 3D magnetohydrodynamics equations

In this article, we establish sufficient conditions for the regularity of solutions of 3D MHD equations in the framework of the anisotropic Lebesgue spaces. In particular, we obtain the anisotropic regularity criterion via partial derivatives, and it is a generalization of the some previous results. Besides, the anisotropic integrability regularity criteria in terms of the magnetic field and the third component of the velocity field are also investigated. Copyright © 2017 John Wiley & Sons, Ltd.     

Nguetseng’s two-scale convergence method for filtration and seismic acoustic problems in elastic porous media

A linear system is considered of the differential equations describing a joint motion of an elastic porous body and a fluid occupying a porous space. The problem is linear but very hard to tackle since its main differential equations involve some (big and small) nonsmooth oscillatory coefficients. Rigorous justification under various conditions on the physical parameters is fulfilled for the homogenization procedures as the dimensionless size of pores vanishes, while the porous body is geometrically periodic. In result, we derive Biot’s equations of poroelasticity, the system consisting of the anisotropic Lamé equations for the solid component and the acoustic equations for the fluid component, the equations of viscoelasticity, or the decoupled system consisting of Darcy’s system of filtration or the acoustic equations for the fluid component (first approximation) and the anisotropic Lamé equations for the solid component (second approximation) depending on the ratios between the physical parameters. The proofs are based on Nguetseng’s two-scale convergence method of homogenization in periodic structures.     

Anisotropic Parabolic Equations with Measure Data

In this paper, we prove the existence of solutions to anisotropic parabolic equations with right hand side term in the bounded Radon measure M(Q) and the initial condition in M(Ω) or in L^m space (with m “small”).     

Boundedness of Solutions to Anisotropic Variational Problems

We investigate the global boundedness of minimizers of fully anisotropic minimum problems for integral functionals of the calculus of variations and of weak solutions to fully anisotropic quasilinear elliptic equations in divergence form.     

A Carleman inequality for the stationary anisotropic Maxwell system

A Carleman estimate for the stationary anisotropic Maxwell system is established. Its proof adopts a technique pioneered by Calderón to an overdetermined systems with rough coefficients. As an application, the conditional stability of the Cauchy problem is discussed.     

三维各向异性Navier-Stokes方程一类大解的整体正则性——献给陆善镇教授75华诞

利用解析性估计和方程非线性项的特殊结构,本文证明了三维各向异Navier-Stokes方程对一类在垂直方向慢变的大初值的整体适定性.     

On a free boundary problem for a class of anisotropic equations

This paper deals with a certain condenser capacity in an anisotropic environment. More precisely, we are going to investigate a free boundary problem for a class of anisotropic equations on a ring domain N≥2. Our aim is to show that if the problem admits a solution in a suitable weak sense, then the underlying domain Ω is a Wulff‐shaped ring. The proof makes use of a maximum principle for an appropriate P‐function, in the sense of L. E. Payne, a Rellich type identity and some geometric arguments involving the anisotropic mean curvature of the free boundary. Copyright © 2016 John Wiley & Sons, Ltd.     

OPTIMIZATION OF ADAPTIVE DIRECT METHOD FOR APPROXIMATE SOLUTION OF INTEGRAL EQUATIONS OF SEVERAL VARIABLES

This paper determines the exact error order on optimization of adaptive directmethods of approximate solution of the class of Fredholm integral equations of the secondkind with kernel belonging to the anisotropic Sobolev classes, and also gives an optimalalgorithm.     

非线性抛物积分微分方程的各向异性有限元高精度分析

本文讨论非线性抛物积分微分方程的各向异性有限元方法.在不引入真解的H1-Volterra投影的情况下得到了半离散格式下的整体超收敛.     

Nonlinear anisotropic parabolic equations in with locally integrable data

In this paper, we prove existence and regularity of weak solutions for a class of nonlinear anisotropic parabolic problems in with locally integrable data. Our approach is based on the anisotropic Sobolev inequality, a smoothness, and compactness results. Copyright © 2012 John Wiley & Sons, Ltd.     

Sobolev方程的一类各向异性非协调有限元逼近

在各向异性网格下,分别讨论了Sobolev方程在半离散和全离散格式下的一类非协调有限元逼近,得到了与传统有限元方法相同的误差估计和一些超逼近性质.同时在半离散格式下,通过构造具有各向异性特征的插值后处理算子得到了整体超收敛结果.     

多元积分方程自适应解法的优化

考虑核属于各向异性的Sobolev类的积分方程自适应直接方法的优化,得到误差阶的精确估计及相应的最优方法.     

非线性波动方程的各向异性有限元方法

研究了非线性波动方程的各向异性有限元方法,得到了半离散格式下的最优误差估计.     

Multigrid Waveform Relaxation for Anisotropic Partial Differential Equations

Multigrid waveform relaxation provides fast iterative methods for the solution of time-dependent partial differential equations. In this paper we consider anisotropic problems and extend multigrid methods developed for the stationary elliptic case to waveform relaxation methods for the time-dependent parabolic case. We study line-relaxation, semicoarsening and multiple semicoarsening multilevel methods. A two-grid Fourier–Laplace analysis is used to estimate the convergence of these methods for the rotated anisotropic diffusion equation. We treat both continuous time and discrete time algorithms. The results of the analysis are confirmed by numerical experiments.     

Analyzing of the effect of the dusty fluid,anisotropy and layered of the wall on the wave propagation

This study considers the propagation of time harmonic waves in, prestressed, anisotropic elastic tubes filled with viscous fluid containing dusty particles. The fluid is assumed to be incompressible and Newtonian. The tube material is considered to be incompressible, anisotropic, and elastic. The tube is subjected to a static inner pressure P_i and an axial stretch λ. Utilizing the theory of “Superposing small deformations on large initial static deformations”, differential equations governing wave propagation inside the tube are obtained in terms of cylindrical coordinates. Analytical solutions for the equations of motion for the dust and the fluid are obtained, and expressed numerically. The dispersion relation is obtained as a function of the stretch, the thickness ratio and the parameters for dusty particles.     

Regularity criteria for the 3D MHD equations in term of velocity

In this paper, we consider three‐dimensional incompressible magnetohydrodynamics equations. By using interpolation inequalities in anisotropic Lebesgue space, we provide regularity criteria involving the velocity or alternatively involving the fractional derivative of velocity in one direction, which generalize some known results. Copyright © 2014 John Wiley & Sons, Ltd.