共查询到20条相似文献,搜索用时 15 毫秒
1.
Salim A. Messaoudi Michael Pokojovy Belkacem Said‐Houari 《Mathematical Methods in the Applied Sciences》2009,32(5):505-534
In this paper, we consider nonlinear thermoelastic systems of Timoshenko type in a one‐dimensional bounded domain. The system has two dissipative mechanisms being present in the equation for transverse displacement and rotation angle—a frictional damping and a dissipation through hyperbolic heat conduction modelled by Cattaneo's law, respectively. The global existence of small, smooth solutions and the exponential stability in linear and nonlinear cases are established. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
2.
The Exact Limits and Improved Decay Estimates for All Order Derivatives of the Global Weak Solutions to a Two-Dimensional Incompressible Dissipative Quasi-Geostrophic Equation 下载免费PDF全文
Linghai Zhang 《Journal of Nonlinear Modeling and Analysis》2023,5(1):146-202
We will accomplish the exact limits for all order derivatives of the global weak solutions to a two-dimensional incompressible dissipative quasi-geostrophic equation. We will also establish the improved decay estimates with sharp rates for all order derivatives. We will consider two cases for the initial function and the external force and prove the optimal results for both cases. We will couple together existing ideas (including the Fourier transformation and its properties, Parseval''s identity, iteration technique, Lebesgue''s dominated convergence theorem, Gagliardo-Nirenberg-Sobolev interpolation inequality, squeeze theorem, Cauchy-Schwartz''s inequality, etc) existing results (the existence of global weak solutions, the existence of local smooth solution on $(T,\infty)$ and the elementary decay estimate with a sharp rate) and a few novel ideas to obtain the main results. 相似文献
3.
该文利用重要不等式及能量积分方法首先得到了解的初等的先验估计.然后利用线性半群的有关性质及精细计算得到了解的最大模估计,从而证明了两类三次自催化模型在Dirichlet边界条件下整体解的存在性,并进而证明了第一类模型的最大吸引子的存在性. 相似文献
4.
Zhaoyun Zhang Bo‐Qing Dong Yan Jia 《Mathematical Methods in the Applied Sciences》2019,42(9):3388-3399
This paper focuses on a system of the two‐dimensional (2D) magnetohydrodynamic (MHD) equations with the partial kinematic dissipation (?yyu1,?xxu2) and the partial magnetic diffusion (?yyb1,?xxb2). Based on the basic energy estimates only, we are able to show that this system always possesses a unique global smooth solution when the initial data are sufficiently smooth. Moreover, we obtain optimal large‐time decay rates of both solutions and their higher order derivatives by developing the classic Fourier splitting methods together with the auxiliary decay estimates of the first derivative of solutions and induction technique. 相似文献
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Peng Qu 《Mathematical Methods in the Applied Sciences》2013,36(12):1520-1532
A kind of partially dissipative quasilinear hyperbolic systems in which a part of equations possesses the strict dissipation and the others are weakly linearly degenerate are discussed. Under some weaker hypotheses on the interactions between two parts of equations, it is proved that for any given initial data with small W1,1 and C1 norms, the corresponding Cauchy problem admits a unique C1 global classical solution. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
8.
ZHANG Ming 《数学季刊》2014,(3):457-464
In this paper we investigate the global attractors for the one-dimensional linear model of thermodiffusion with second sound. Using the method of contractive functions, we obtain the asymptotically compact of the semigroup and the existence of the global attractors Key words: thermodiffusion~ second sound; globat attractors, asymptotically compact 相似文献
9.
用罚函数求解线性双层规划的全局优化方法 总被引:6,自引:0,他引:6
用罚函数法将线性双层规划转化为带罚函数子项的双线性规划问题,由于其全局最优解可在约束域的极点上找到,利用对偶理论给出了一种求解该双线性规划的方法,并证明当罚因子大于某一正数时,双线性规划的解就是原线性双层规划的全局最优解。 相似文献
10.
The paper studies the existence,the exponential decay and the nonexistence of global solution for a class of quasilinear parabolic equations. 相似文献
11.
Salim A. Messaoudi 《Mathematical Methods in the Applied Sciences》2005,28(15):1819-1828
In this paper, we consider the non‐linear wave equation a,b>0, associated with initial and Dirichlet boundary conditions. Under suitable conditions on α, m, and p, we give precise decay rates for the solution. In particular, we show that for m=0, the decay is exponential. This work improves the result by Yang (Math. Meth. Appl. Sci. 2002; 25 :795–814). Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
12.
Global existence of weak discontinuous solutions to the Cauchy problem with small BV initial data for quasilinear hyperbolic systems 下载免费PDF全文
Libin Wang 《Mathematical Methods in the Applied Sciences》2015,38(5):966-979
In this paper, we study the Cauchy problem for quasilinear hyperbolic system with a kind of non‐smooth initial data. Under the assumption that the initial data possess a suitably small bounded variation norm, a necessary and sufficient condition is obtained to guarantee the existence and uniqueness of global weak discontinuous solution. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
13.
In this work we study some properties of solutions for the systemdescribing a three-dimensional non-homogeneous non-conductingdielectric with a general boundary condition with memory. Wefirst show the existence of the inverse of this boundary condition,which allows us to introduce a boundary free energy, similarto the one considered by Fabrizio & Morro (1996, Arch. Rat.Mech. Anal., 136, 359381). Then, we prove existence anduniqueness theorems for weak and strong solutions of the evolutiveproblem in a finite time interval. Moreover, following Rivera& Olivera (1997, Boll. U.M.I., 11-A, 115127), weexamine some dissipative properties of the boundary conditionand of its inverse and we give a useful energy estimate. Finally,when there is no memory in the boundary condition the exponentialdecay of the solution is proved. 相似文献
14.
罗兰 《纯粹数学与应用数学》2012,28(3):313-328
主要研究带有Gilbert阻尼项的Landau-Lifshitz铁磁链方程的柯西问题.当初值的一阶导数适当小时,基于加权能量估计,证明了强解的整体存在性并且给出了解的最优的L2和L∞衰减估计. 相似文献
15.
We study the initial boundary value problem to the system of the compressible Navier-Stokes equations coupled with the Maxwell equations through the Lorentz force in a bounded annulus Ω of R3. And a result on the existence and uniqueness of global spherically symmetric classical solutions is obtained. Here the initial data could be large and initial vacuum is allowed. 相似文献
16.
Global Existence of Solutions for the Cauchy Problem of the Kawahara Equation with L
2 Initial Data 总被引:6,自引:0,他引:6
Shang Bin CUI Dong Gao DENG Shuang Ping TAO 《数学学报(英文版)》2006,22(5):1457-1466
In this paper we study solvability of the Cauchy problem of the Kawahara equation 偏导dtu + au偏导dzu + β偏导d^3xu +γ偏导d^5xu = 0 with L^2 initial data. By working on the Bourgain space X^r,s(R^2) associated with this equation, we prove that the Cauchy problem of the Kawahara equation is locally solvable if initial data belong to H^r(R) and -1 〈 r ≤ 0. This result combined with the energy conservation law of the Kawahara equation yields that global solutions exist if initial data belong to L^2(R). 相似文献
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讨论了一类带阻尼项的n维Klein Gordon方程的柯西问题,观察到其线性方程的耗散结构是正则耗散型,这将意味着在对初值的正则假设下,可以得到解的最佳衰减估计.基于其相应线性方程的衰减估计和小初值条件,利用压缩映射原理,在Sobolev空间中证明了整体解的存在性和小振幅解的渐近行为. 相似文献
18.
Global Solutions in L^infinity for a System of Conservation Laws of Viscoelastic Materials with Memory 下载免费PDF全文
We construct global solutions in L^∞ for the equations of motion or one-dimensional viscoelastic media, in Lagrangian coordinates, with arbitrarily large L^∞ initial data, via the vanishing viscosity method. A priori estimates for approximate solutions, with artificial viscosity, are derived through entropy inequalities. The convergence of the approximate solutions to a weak solution compatible with the entropy condition is demonstrated. This also establishes the compactness of the corresponding solution operators, which indicates that the memory effect does not affect the hyperbolic behavior. 相似文献
19.
我们考虑如下方程的整体解的存在性:uxt 3/2ux^2uxx Uxxxx-sinu εux=f我们先给出了一致性先验估计,然后在H0^1∩H^2空间证明了整体解的存在性. 相似文献
20.
This article is devoted to the study of global existence and exponential stability of solutions to an initial-boundary value problem of the quasilinear thermo-diffusion equations with second sound by means of multiplicative techniques and energy method provided that the initial data are close to the equilibrium and the relaxation kernel is strongly positive definite and decays exponentially. 相似文献