共查询到20条相似文献,搜索用时 15 毫秒
1.
Paweł Konieczny 《Acta Appl Math》2009,106(1):61-77
The paper examines the issue of existence of solutions to the steady Navier-Stokes equations in an exterior domain in ℝ2. The system is studied with nonhomogeneous slip boundary conditions. The main results proves the existence of weak solutions
for arbitrary data.
相似文献
2.
Simulations of blood flows in arteries require numerical solutions
of fluid-structure interactions involving Navier-Stokes equations
coupled with large displacement visco-elasticity for the vessels.
Among the various simplifications which have been proposed, the
surface pressure model leads to a hierarchy of simpler models
including one that involves only the pressure. The model exhibits
fundamental frequencies which can be computed and compared with the
pulse. Yet unconditionally stable time discretizations can be
constructed by combining implicit time schemes with
Galerkin-characteristic discretization of the convection terms in
the Navier-Stokes equations. Such problems with prescribed pressure
on the walls will be shown to be efficient and accurate as an
approximation of the full fluid structure interaction problem. 相似文献
3.
The boundary control problem of an elastic thin plate with boundary viscoelasticity is formulated in the standard form of a linear infinite-dimensional systems in the energy Hilbert space. The feedback control is designed so that the input and output are collocated. The frequency-domain approach is adopted in investigating the exponential stability of the closed-loop system. Finally, by considering the boundary viscoelasticity as damping, we establish a strong stability result based on the LaSalle invariance principle and the Hömander uniqueness theorem. 相似文献
4.
J. Karátson 《Numerical Functional Analysis & Optimization》2013,34(5-6):590-611
The superlinear convergence of the preconditioned CGM is studied for nonsymmetric elliptic problems (convection-diffusion equations) with mixed boundary conditions. A mesh independent rate of superlinear convergence is given when symmetric part preconditioning is applied to the FEM discretizations of the BVP. This is the extension of a similar result of the author for Dirichlet problems. The discussion relies on suitably developed Hilbert space theory for linear operators. 相似文献
5.
L. V. Dorodnitsyn 《Computational Mathematics and Modeling》2003,14(3):246-276
External problems of fluid dynamics are modeled on artificially bounded regions. A method is proposed for applying nonreflecting boundary conditions to the linearized Euler equations obtained from the original nonlinear problem. The nonreflecting conditions are modified to allow for viscosity and nonhomogeneity of unperturbed background flow in linear Euler, Navier–Stokes, and quasi-fluid-dynamic models. One-dimensional test problems are computed in the linear and nonlinear cases. 相似文献
6.
基于物理学基本原理和能量守恒定律的精确检查,导出充满黏性流体多孔固体边界呈连续性要求的边界条件.当孔隙流体具有黏性时,多孔弹性固体就是一个耗散的充满黏性流体的多空固体.孔隙流体的黏性造成的耗散应力准确地表达了边界条件.边界上两种固体连接的不完全,导致孔隙流体的流出,多孔骨料两边微粒运动的不平衡.导出多孔.多孔固体界面孔隙局部连接时的数学模型.在该界面上,滑移的松.紧,以及孔隙开.合,能造成一部分应变能的耗散.数值结果表明,在水和饱和油砂岩之间的界面上,修正的边界条件将影响各向同性多孔介质中折射波的能量. 相似文献
7.
H. Beirão da Veiga 《Acta Appl Math》2014,132(1):63-71
These notes concern the study of sufficient conditions on the direction of the vorticity to guarantee regularity of solutions to the evolution Navier–Stokes equations. We emphasize here some thread lines of the research, taken as a whole. Interdependence among distinct results and techniques is discussed. We end by a sketch of the proof of a quite recent result. 相似文献
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本文是[1]的继续.在本文中,利用[1]的结果我们证明了,对于流体的层流运动稳定性而言,在线性化问题中,按特征值定义与按扰动能量定义二者是完全等价的,从外,借助于Ляпунов方法,我们又证明了,如果线性化问题是渐近稳定的,当考虑非线性影响时,只要扰动能量足够小,则仍然是渐近稳定的. 相似文献
10.
General Energy Decay for a Viscoelastic Equation of Kirchhoff Type with Acoustic Boundary Conditions
This paper is concerned with a viscoelastic equation of Kirchhoff type with acoustic boundary conditions in a bounded domain of \(\mathbb {R}^{n}.\) We show that, under suitable conditions on the initial data, the solution exists globally in time. Then, we prove the general energy decay of global solutions by applying a lemma of Martinez, which allows us to get our decay result for a class of relaxation functions wider than that usually considered. 相似文献
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12.
本文考虑形如的非线性四阶微分方程非局部边值问题,这里a,b∈L~1[0,1],g:(0,1)→[0,∞)在(0,1)上连续、对称,且可能在t=0和t=1处奇异.f:[0,1]×[0,∞)→[0,∞)连续且对所有x∈[0,∞],f(·,x)在[0,1]上对称.在某些适当的增长性条件下,应用Krasnoselskii不动点定理证明了对称正解的存在性和多重性. 相似文献
13.
14.
Let x=g(t,x(t),u(t)) be the governing equation of an optimal control problem with two-point boundary conditions h
0(x(a))+h
1(x(b)) = 0, where x: [a,b]
n
is continuous, u: [a,b]
k-n
is piecewise continuous and left continuous, h0,h1:
n
q
are continuously differentiable, and g:[a,b]×
k
n
is continuous. The paper finds functions
i
C1([a,b]×
n
) such that (x(t),u(t)) is a solution of the governing equation if and only if
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15.
Daniel Baffet 《Applied Numerical Mathematics》2011,61(6):768-784
The Higdon sequence of Absorbing Boundary Conditions (ABCs) for the linear wave equation is considered. Building on a previous work of Ha-Duong and Joly, which related to other forms of boundary conditions, the Higdon ABCs are proved to be energy-stable (on the continuous level) up to any order. This type of stability is stronger than the more standard notion of stability of initial boundary value problems in the sense of Kreiss; in particular it leads to stability estimates which are uniform in time. In consequence to the theorem proved here, energy-stability is immediately implied for the high-order Givoli-Neta and Hagstrom-Warburton ABCs, which are reformulations of the Higdon ABCs using auxiliary variables. A weakness of this theory is that it requires sufficiently smooth data, and that the required smoothness level increases with the order of the ABC. This issue and its implications are discussed. 相似文献
16.
In this paper, we consider a viscoelastic equation of variable coefficients in the presence of infinite memory (past history) with nonlinear damping term and nonlinear delay term in the boundary feedback and acoustic boundary conditions. Under suitable assumptions, two arbitrary decay results of the energy solution are established via suitable Lyapunov functionals and some properties of the convex functions. The first stability result is given with relation between the damping term and relaxation function. The second result is given without imposing any restrictive growth assumption on the damping term and the kernel function \(g\). Our result extends the decay result obtained for problems with finite history to those with infinite history. 相似文献
17.
Mathematical Notes - In this paper, we consider the nonlinear viscoelastic Kirchhoff-type equation $${u_{tt}} - M(||\nabla u||_2^2)\Delta u + \int_0^t {h(t - s)\Delta u(s)ds + a|{u_t}{|^{m -... 相似文献
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D. J. Benney 《Studies in Applied Mathematics》1966,45(1-4):52-63