共查询到20条相似文献,搜索用时 15 毫秒
1.
We prove the global existence and regularity of weak solution for the 2-D liquid crystal flows with the large initial velocity. The uniqueness of weak solution is also proved by using the Littlewood–Paley analysis. 相似文献
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The qualitative dynamics of weak solutions to a nonautonomous model of polymer solution motion (with a rheological relation satisfying the objectivity principle) is studied using the theory of pullback attractors of trajectory spaces. For this purpose, the existence of weak solutions is proved for the model under study, a family of trajectory spaces is defined, trajectory and minimal pullback attractors are introduced, and their existence is proved. 相似文献
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This paper studies the problem for optimal control of the viscous DGH equation. The existence and uniqueness of weak solution to the equation are proved in a short interval. The optimal control of the viscous DGH equation under boundary condition is given and the existence of optimal solution to the equation is proved. 相似文献
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P. Colli G. Gilardi M. Grasselli 《NoDEA : Nonlinear Differential Equations and Applications》1997,4(1):123-132
A model for Stefan problems in materials with memory is considered. This model is mainly characterized by a nonlinear Volterra
integrodifferential equation of hyperbolic type. Colli and Grasselli proved the uniqueness of a weak solution under the natural
assumptions on data and the existence of a strong solution for smoother data. Taking advantage of these two results and assuming
just the hypotheses ensuring uniqueness, the existence of a weak solution is here shown.
Received October 19, 1995 相似文献
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The Existence and Long-Time Behavior of Weak Solution to Bipolar Quantum Drift-Diffusion Model 总被引:1,自引:0,他引:1 下载免费PDF全文
Xiuqing CHEN~* Li CHEN~ 《数学年刊B辑(英文版)》2007,28(6):651-664
The authors study the existence and long-time behavior of weak solutions to the bipolar transient quantum drift-diffusion model,a fourth order parabolic system.Using semi-discretization in time and entropy estimate,the authors get the global existence of nonnegative weak solutions to the one-dimensional model with nonnegative initial and homogenous Neumann(or periodic)boundary conditions.Furthermore,by a logarithmic Sobolev inequality,it is proved that the periodic weak solution exponentially approaches its mean value as time increases to infinity. 相似文献
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Le Thi Phuong Ngoc Nguyen Anh Triet Nguyen Thanh Long 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(3-4):1865-1885
The paper is devoted to the study of a linear wave equation with a nonlinear boundary condition of viscoelastic type. The existence of a weak solution is proved by using the Faedo–Galerkin method. The uniqueness, regularity and asymptotic expansion of the solution are also discussed. 相似文献
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该文研究了一个适合应用于天气预报的大气模型,模型考虑到地形对大气的动力强迫作用,保留了大气气流的辐散效应.首先采用了适当的函数空间,引入了合理的算子表达形式,将复杂的大气动态方程组用一个简单的抽象的算子方程表示,由此给出了模型弱解的定义.然后利用Galerkin方法证明了弱解的存在性.通过构造大气动态方程组轨道吸引集证明相应的轨道吸引子的存在性. 相似文献
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We proved existence, regularity and uniqueness of steady subsonic potential flows in n-dimensional (n ≥ 3) infinite nozzles with largely-open convergent and divergent parts when the total mass flux is less than a certain value. Such nozzles consist of two cones with arbitrary open angles and an arbitrary smooth bounded tubular part. The existence of a weak solution is proved by applying the direct method of calculus of variation to a carefully chosen functional defined on a Hilbert space based upon Hardy inequality. Hölder gradient regularity of weak solution is shown by using Moser iteration to quasilinear elliptic equations in divergence form. Also, the obtained solution is unique in the class of functions with finite kinetic energy by modulo a constant. 相似文献
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Euler-Bernoulli粘弹性方程初边值问题整体解的存在性 总被引:1,自引:0,他引:1
本文利用 Faedo- Galerkin方法证明了一类具记忆项的 Euler- Bernoulli粘弹性方程初边值问题整体解的存在性 . 相似文献
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Qiang Chang Ju 《数学学报(英文版)》2009,25(2):253-264
Semiclassical limit to the solution of isentropic quantum drift-diffusion model in semicon- ductor simulation is discussed. It is proved that the semiclassical limit of this solution satisfies the classical drift-diffusion model. In addition, we also proved the global existence of weak solutions. 相似文献
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本文按照Grad~([6])指出的方法具体地证明了弱非线性、弱涨落的Boltzmann方程链的经典解的存在性. 相似文献
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A. A. Petrosyan G. S. Hakobyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2008,43(2):118-125
The paper studies a generalization of the pseudoparabolic variational inequalities. The existence and uniqueness of the solution of the corresponding weak problem and the regularity of the obtained solution are proved. 相似文献
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A. E. Kovtanyuk A. Yu. Chebotarev 《Computational Mathematics and Mathematical Physics》2014,54(4):719-726
The problem of radiative-conductive-convective heat transfer in a three-dimensional domain is studied. The existence of a weak solution of the problem is proved, and sufficient conditions for the uniqueness of a solution are found. The temperature distribution in a three-dimensional channel is determined in numerical experiments. 相似文献
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Summary
This paper considers the existence of optimal controls for systems governed by a second order parabolic partial differential equation in divergence form with Cauchy conditions. As preliminary results, theorems concerning the convergence of the sequence of weak solutions corresponding to a sequence of admissible controls are proved. Two general forms of criteria are considered. The first one is taken as a function of the weak solution of the system, and the other is taken as a function of the solution of the system and control. Several theorems and corollaries on the existence of optimal controls are then presented. 相似文献
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Arnon Levy 《偏微分方程通讯》2013,38(3-4):657-698
Majda's model of dynamic combustion, consists of the system, In this paper the Cauchy problem is considered. A weak entropy solution for this system is defined, existence, uniqueness and continuous dependence on initial data are proved, as well as finite propagation speed, for initial data in . The existence is proved via the "vanishing viscosity method". Furthermore it is proved that the solution to the Riemann problem converges as to the Z–N–D traveling wave solution. In the appendices, a second order numerical scheme for the model is described, and some numerical results are presented. 相似文献
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The existence of weak solution is proved for a Langevin type second-order stochastic differential inclusion on a complete Riemannian manifold, having both drift and diffusion terms set-valued. The construction of solution involves integral operators with Riemannian parallel translation and a special sequence of continuous ?-approximations for an upper semicontinuous set-valued mapping with convex bounded closed values, that is proved to converge point-wise to a Borel measurable selection. 相似文献
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杨力平 《应用数学学报(英文版)》1994,10(3):233-251
FREEBOUNDARYPROBLEMARISINGFROMEVAPORATIONFROMPOROUSMEDIUMYANGLIPING(杨力平)(DepartmentofAppliedMathematics,TsinghuaUniversity,Be... 相似文献