共查询到10条相似文献，搜索用时 31 毫秒
1.
The long time behavior of solution of the Hasegawa-Mima equation with dissipation term was considered. The global attractor problem of the Hasegawa-Mima equation with initial periodic boundary condition was studied. Applying the uniform a priori estimates method, the existence of global attractor of this problem was proved, and also the dimensions of the global attractor was estimated. 相似文献
2.
LetGbeaboundeddomaininthen-dimensionEuclideanspaceE\",I相似文献
3.
We present and analyse a new mixed finite element method for the generalized Stokes problem. The approach, which is a natural extension of a previous procedure applied to quasi‐Newtonian Stokes flows, is based on the introduction of the flux and the tensor gradient of the velocity as further unknowns. This yields a two‐fold saddle point operator equation as the resulting variational formulation. Then, applying a slight generalization of the well known Babu?ka–Brezzi theory, we prove that the continuous and discrete formulations are well posed, and derive the associated a priori error analysis. In particular, the finite element subspaces providing stability coincide with those employed for the usual Stokes flows except for one of them that needs to be suitably enriched. We also develop an a posteriori error estimate (based on local problems) and propose the associated adaptive algorithm to compute the finite element solutions. Several numerical results illustrate the performance of the method and its capability to localize boundary layers, inner layers, and singularities. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
4.
In the paper we give a proof of the global existence of the weak solution to the initial-boundary-value problem describing an incompressible elasto-viscous-multipolar material in finite geometry. A brief introduction to the physical background of viscous-multipolar materials is given. We suggest the hypothesis% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaamaaxadabaGaeu4OdmfaleaacaWGPbGaaiilaGqaciaa-bcacaWG% QbGaa8hiaiabg2da9iaa-bcacaaIXaaabaGaaG4maaaakiaa-bcada% abdiqcaasaaOWaaSaaaKaaGeaacqGHciITcqqHOoqwcaGGOaGaamOr% aiaacYcacqaH4oqCcaGGPaaabaGaeyOaIyRaamOraOWaaSbaaSqaai% aadMgacaWGbbaabeaaaaqcaaIaa8hiaiaadAeakmaaBaaaleaacaWG% QbGaamyqaaqabaaajaaqcaGLhWUaayjcSdGaa8hiaiabgsMiJkaado% gakmaaBaaaleaacaWFVbaabeaakiaadwgacaGGOaGaamOraiaacYca% ieaacaGFGaGaeqiUdeNaaiykaiaa+bcacqGHRaWkcaGFGaGaam4yam% aaBaaaleaacaaIXaGaa4hiaiaacYcaaeqaaaaa!686E!\[\mathop \Sigma \limits_{i, j = 1}^3 \left| {\frac{{\partial \Psi (F,\theta )}}{{\partial F_{iA} }} F_{jA} } \right| \leqslant c_o e(F, \theta ) + c_{1 ,} \] which enables one to obtain a priori estimates. 相似文献
5.
The dissipative quantum Zakharov equations are mainly studied. The existence and uniqueness of the solutions for the dissipative quantum Zakharov equations are proved by the standard Galerkin approximation method on the basis of a priori estimate. Meanwhile, the asymptotic behavior of solutions and the global attractor which is constructed in the energy space equipped with the weak topology are also investigated. 相似文献
6.
林宗池 《应用数学和力学(英文版)》1980,1(3):357-370
This paper is the continuation of article [7]. It gives further results about the asymptotic expression for the solution of higher order elliptic equation in the case of boundary perturbation combined with operator perturbation. When unperturbed problemA0 is not on the spectrum, the asymptotic expression for the solution of perturbation problemA may be expanded with respect to the small parameter . WhileA0 is on the spectrum, the asymptotic expression of the solution contains negative powers of the small parameter . The approximation of arbitrary order to the solution is considered and the recursive formula for the general term and the estimation of remainder term are given. 相似文献
7.
ＡＰＲＩＯＲＩＥＳＴＩＭＡＴＥＳＴＯＴＨＥＭＡＸＩＭＵＭＭＯＤＵＬＵＳＯＦＧＥＮＥＲＡＬＩＺＥＤＳＯＬＵＴＩＯＮＳＯＦＡＣＬＡＳＳＯＦＱＵＡＳＩＬＩＮＥＡＲＥＬＬＩＰＴＩＣＥＱＵＡＴＩＯＮＳＷＩＴＨＡＮＩＳＯＴＲＯＰＩＣＧＲＯＷＴＨＣＯＮＤＩＴＩＯＮ... 相似文献
8.
Let G be a bounded domain in E~n.Consider the following quasi-linear elliptic equationAlthough the boundedness of generalized solutions of the equation is proved for very generalstructural conditions,it does not supply a priori estimate for maximum modulus ofsolutions.In this paper an estimate to the maximum modulus is made firstly for a specialcase of quasi-linear elliptic equations,i.e.the(?)and B satisfy the following structuralconditions: 相似文献
9.
The delay differential equation,
(t)=–x(t)+f(x(t–1)), with >0 and a real function f satisfying f(0)=0 and f>0 models a system governed by delayed positive feedback and instantaneous damping. Recently the geometric, topological, and dynamical properties of a three-dimensional compact invariant set were described in the phase space C=C([–1, 0], ) of initial data for solutions of the equation. In this paper, for a set of and f which include examples from neural network theory, we show that this three-dimensional set is the global attractor, i.e., the compact invariant set which attracts all bounded subsets of C. The proof involves, among others, results on uniqueness and absence of periodic orbits. 相似文献
10.
Dalibor Pražák 《Journal of Dynamics and Differential Equations》2002,14(4):763-776
We prove that the global attractor to a semilinear damped wave equation has finite fractal dimension provided that the damping function and the lower order nonlinearity are smooth with certain polynomial growth. 相似文献