一类三阶梯度流方程弱解的稳定性[英文]

本文研究R~3上的一类三阶梯度流方程弱解的稳定性问题.我们分别证明弱解的一个全局稳定性结果和一个渐近稳定性结果.所得结果改进了已有文献中的一些关于三阶梯度流方程弱解的稳定性结果.     

拟线性次椭圆方程很弱解的正则性

该文利用扰动向量场的Hodge分解及估计构造关于弱解X梯度场的反向Hlder不等式,从而建立了Carnot群上的散度型拟线性次椭圆方程很弱解梯度的可积性指数的提高,得到其很弱解是经典意义的弱解结论.     

基于变分方法的奇异脉冲方程弱解的存在性

该文研究了一类具有扰动项的非线性奇异脉冲微分方程边值问题,利用变分方法结合临界点理论得到了弱解的存在性定理.     

一维活塞问题激波解的整体存在性

本文用改进的Glimm格式的方法,研究一维活塞问题当活塞的运动速度是一个常数的扰动时含有激波的弱解的存在性.对波的相互作用以及扰动波在主激波和活塞上的反射作出了精确的估计,在对主激波的强度不加限制的情况下证明了激波解的整体存在性.     

一维活塞问题激波解的整体存在性

本文用改进的Glimm格式的方法,研究一维活塞问题当活塞的运动速度是一个常数的扰动时含有激波的弱解的存在性.对波的相互作用以及扰动波在主激波和活塞上的反射作出了精确的估计,在对主激波的强度不加限制的情况下证明了激波解的整体存在性.     

一类非牛顿系统在三维无界区域中弱解的存在性(英文)

本文考虑一类非牛顿系统在三维无界区域中解的情况 ,证明了当f∈L2 ( 0 ,T ;H)时弱解的存在性 ;当f∈L∞( 0 ,∞ ;H)时弱解的全局存在性 .     

非自治Caputo分数阶发展方程弱解的适定性与不变集

该文分析一族含有依赖时间参数t线性算子的时间分数阶非自治发展方程,利用Lions表示定理,得到了弱解适定性的充分条件;基于正交投影,建立了时间分数阶发展方程弱解的不变性准则.该文所研究方程中的算子是依赖时间的.     

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.     

一类非线性退化椭圆型偏微分方程Dirichlet问题的非平凡弱解

王传芳在文［１］中研究了一类非线性退化椭圆方程－Ｄｉ（ｘ１ｍａ·Ｄｉｕ）＝｜ｕ｜ｓ－１·ｕ＋ｈ（ｘ）的Ｄｉｒｉｃｈｌｅｔ问题，建立了一套指数ｐ＝２的带权Ｓｏｂｏｌｅｖ空间及其嵌入和嵌入紧性理论，用扰动方法得到问题无穷多解的存在性．本文将此理论推广到指数Ｐ≥２的情形，据此推广了的理论研究一类非线性退化椭圆方程－Ｄｉ（｜ｘｍ｜ａ·｜Ｄｕ｜ｐ－２·Ｄｉｕ）＝ｆ（ｘ，ｕ）的Ｄｉｒｉｃｈｌｅｔ问题．利用临界点理论得到问题的非平凡弱解及无穷多个非平凡弱解．同时对解的不存在性进行了讨论．     

一类退缩非线性自由边值问题弱解的存在唯一性

本文研究了由非牛顿流体流动引起的一类退缩非线性自由边值问题.利用Steklov平均函数、先验估计和极限方法,证明了此自由边值问题存在唯一弱解.     

Numerical simulation of flow of viscoelastic fluids

The paper deals with the numerical calculation of highly viscous, non-newtonian fluid flows in apparatus of mechanical engineering. We use a differential constitutive equation to approximate the real behaviour of technical fluids like polymer melts. By means of calculated flow examples in two and three dimensional geometries we demonstrate the influence of the non-newtonian behaviour. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Advanced FEM for free surface flow with application to landslides

An advanced space-time finite element method is presented to investigate movements of landslides and their interaction with flexible structures. The mechanics of liquefied soil is described by Navier-Stokes-equations for visco-plastic non-newtonian fluid. Likewise the fluid the kinematics of the structure is described by velocities, taking large rotations into account. This leads to a monolithic fluid-structure interaction approach considering the multi-field problem as a whole. The discretized model equations are assembled in a single set of algebraic equations, which are solved by applying Newton-Raphson scheme. Free surface motion of landslide is described by the level-set method. To reduce computational effort the fragmented finite element method is used, where only active finite elements are evaluated. A pde-based extrapolation of the velocity-field is applied to ensure an accurate transport of distance function, which defines the profile in space and time of the free surfaces. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

非牛顿多方渗流方程Cauchy问题的可解性

本文讨论非牛顿多方渗流方程初始迹为测度时Ｃａｕｃｈｙ问题的可解性（当ｍ（ｐ—１）＜１时）．     

Numerical simulation of the filling behavior of a Non-Newtonian Fluid

A numerical model for free surface flows of non-newtonian liquids which are injected into a cavity is presented. These flows are regarded as a basic model of injection molding. Model experiments of the injection process are performed with a water-based gel. The flow equations are integrated according to the finite-volume-method. The volume of fluid method (VoF) is employed in order to describe the free surface flow of two incompressible phases, the phase interface is resolved by the method of geometric reconstruction. The Herschel-Bulkley model is used in order to describe shear-thinning behavior of the molding material and the effects of a yielding point. Different patterns of the filling flow depending on the injection parameters are evident in the experiment and the simulation. They are characterized and arranged with respect to the similarity parameters of the flow. Again, the results of the simulation are found to agree well with the experimental observations. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fluid-Structure-Interaction-Analysis concerning Damping Features of Viscous Fluids

This work deals with Fluid-Structure-Interaction (FSI) concerning damping characteristics of viscous liquids, which are investigated to make the offshore structures more secure and efficient. On that account, we modeled a damping element prototype consisting essentially of an elastic cover that is attached to the cylindrical mono pile foundation at the height of waves. Within the framework of FSI, the impact of breaking waves on a three-dimensional model of a damping element prototype corresponding to [1] is simulated. In order to measure the influence of different liquid properties on the damping of the impact, the calculations are set up using newtonian and non-newtonian fluids with varying viscosity. For the non-newtonian investigation verification is carried out with a CFD model. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Solution of the boundary value problem for the equations of steady-state flow of a viscous incompressible nonisothermal fluid past a heated rigid spherical particle

We obtain an analytical solution of a boundary value problem for a viscous incompressible nonisothermal fluid assuming an exponential–power law dependence of the fluid viscosity on temperature. A uniqueness theorem for the Navier–Stokes equation linearized with respect to the velocity is proved. We obtain expressions for the mass velocity components and pressure. The solution of the boundary value problem is sought in the form of an expansion in Legendre polynomials.     

Global in time solutions for the Poiseuille flow of Oldroyd type in 3D domains

A Poiseuille flow in a 3D cylindrical domain is considered for a non-newtonian fluid of Oldroyd type. We prove existence (and uniqueness) of a global (in time) weak solution. Moreover, this weak solution is a strong solution when data are more regular. These results have already been obtained in the case of two concentrical cylinders ([3]). Now, we consider an extension to an unique cylinder. Then, a mixed parabolic-hyperbolic PDE's system appears but the parabolic equation is of degenerate type. The key of the proofs is to estimate in appropriate Sobolev weighted spaces (and to obtain strong convergence in weak norms by means of a Cauchy argument).

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Sunto In questo lavoro viene considerato il moto di Poiseuille in un dominio cilindrico tridimensionale per un fluido non-Newtoniano tipo Oldroyd. Viene dimostrata l'esistenza e l'unicità di una soluzione debole, globale nel tempo. Inoltre, questa soluzione debole diviene forte quando i dati diventano più regolari. Questi risultati sono già noti nel caso del dominio tra due cilindri concentrici ([3]). Qui consideriamo l'estensione ad un unico cilindro. Si ottiene, in questo caso, un sistema di equazioni alle derivate parziali misto parabolico-iperbolico, dove l'equazione parabolica è però di tipo degenere. Il punto chiave delle dimostrazioni consiste nel fornire delle stime in un appropriato spazio di Sobolev pesato ed ottenere convergenza forte nelle norme deboli mediante un argomento alla Cauchy.

     

On a non-isothermal,non-Newtonian lubrication problem with Tresca law: Existence and the behavior of weak solutions

We consider a problem describing the motion of an incompressible, non-isothermal, and non-Newtonian fluid in a three-dimensional thin domain. We first establish an existence result for weak solutions of this problem. Then we study the asymptotic analysis when one dimension of the fluid domain tends to zero. A specific weak Reynolds equation, the limit of Tresca fluid–solid boundary conditions, and the limit boundary conditions for the temperature are obtained. The uniqueness result for the limit problem is also proved.     

Fluid models of many-server queues with abandonment

We study many-server queues with abandonment in which customers have general service and patience time distributions. The dynamics of the system are modeled using measure-valued processes, to keep track of the residual service and patience times of each customer. Deterministic fluid models are established to provide a first-order approximation for this model. The fluid model solution, which is proved to uniquely exist, serves as the fluid limit of the many-server queue, as the number of servers becomes large. Based on the fluid model solution, first-order approximations for various performance quantities are proposed.     

Solvability in the large on (0, ∞) of the fundamental initial-boundary value problem for the two-dimensional equations of the motion of Oldroyd fluids

The unqiue global solvability for t (0, ) is proved for the system describing the two-dimensional motion of an Oldroyd fluid.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 156, pp. 69–72, 1986.