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971.
在已知大气运动基本方程于光滑函数类中具有最好的稳定性前提下,讨论了它的局部解的解空间构造.根据它的解空间构造,分析了这个方程具有代表性和应用性的第三初值问题,在解析函数类中给出了适定的第三初值问题的解析解的计算方法以及具体的关系表达式,在局部解意义下完整的解决了这一点初值问题的解析解所涉及的理论与计算问题.指出其它类型定解问题都可以仿照文中的计算方法和步骤,求出所需要的稳定的解析解.  相似文献   
972.
Self-diffusion coefficients of Li+ DLi+, PF6 DPF6 and solvent propylene carbonate (PC) DPC in LiPF6−PC solutions were determined at 298 K by the pulse gradient spin echo (PGSE) NMR technique over the salt concentration range of 0.1–3.0 M (M = mol dm– 3). The order of the diffusion coefficients was found to be DLi+ < DPF6 < DPC over the concentration range examined, and they were monotonically decreased with increasing the salt concentration. Haven ratio Λ/ΛNMR, where Λ and ΛNMR represent the ionic conductivity measured electrochemically and that estimated via the Nernst-Einstein equation using the diffusion coefficient, respectively, was evaluated as the measure of the ion–ion interaction in the LiPF6–PC solutions. Though Λ/ΛNMR values for LiPF6-solutions decrease with increasing the salt concentration, they were greater than those for LiBF4–PC solutions over the whole concentration range examined, which indicates that the ion pair formation ability of PF6 ion is weaker than that of the BF4 ion. The smaller value of the ionic conductivity for the highly concentrated LiPF6–PC solution (above 2.0 M) than that of the LiBF4-solutions can be attributed to the more rapidly increased viscosity relative to the LiBF4-solution. Classic molecular dynamics (MD) simulations for the respective LiPF6 and LiBF4-solution of 0.5 and 1.0 M were also carried out based on the effective pair potentials. Diffusion coefficients, ionic conductivity and Haven ratio for these solutions were calculated from MD trajectories, and they qualitatively agree with those evaluated by experiments. Pair correlation functions gLiO(r) (for Li+–O (PC) pair) and gLiPF6(r) (for Li+–PF6 pair) or gLiBF4(r) (for Li+–BF4 pair) revealed that the lithium ion weakly forms the contact ion pairs with PF6, whilst strongly with BF4, which supports the present experimental results. Moreover, the simulation results show that both anions in the contact ion pairs predominantly take the monodentate form, which is in contrast to the multidentate coordination predicted by ab initio calculation in gas phase.  相似文献   
973.
The symmetries, symmetry reductions, and exact solutions of a coupled nonlinear Schrodinger (CNLS) equation derived from the governing system for atmospheric gravity waves are researched by means of classical Lie group approach in this paper. Calculation shows the CNLS equation is invariant under some Galilean transformations, scaling transformations, phase shifts, and space-time translations. Some ordinary differential equations are derived from the CNLS equation. Several exact solutions including envelope cnoidal waves, solitary waves and trigonometric function solutions for the CNLS equation are also obtained by making use of symmetries.  相似文献   
974.
We restrict our attention to the discrete two-dimensional monatomic β-FPU lattice. We look for two- dimensional breather lattice solutions and two-dimensional compact-like discrete breathers by using trying method and analyze their stability by using Aubry's linearly stable theory. We obtain the conditions of existence and stability of two-dimensional breather lattice solutions and two-dimensional compact-like discrete breathers in the discrete two- dimensional monatomic β-FPU lattice.  相似文献   
975.
976.
We present some new regularity criteria for “suitable weak solutions” of the Navier-Stokes equations near the boundary in dimension three. We prove that suitable weak solutions are Hölder continuous up to the boundary provided that the scaled mixed norm with 3/p+2/q?2, 2<q?∞, (p,q)≠(3/2,∞) is small near the boundary. Our methods yield new results in the interior case as well. Partial regularity of weak solutions is also analyzed under some additional integral conditions.  相似文献   
977.
In this paper, we study the nonlinear one-dimensional periodic wave equation with x-dependent coefficients u(x)ytt−(ux(x)yx)+g(x,t,y)=f(x,t) on (0,πR under the boundary conditions a1y(0,t)+b1yx(0,t)=0, a2y(π,t)+b2yx(π,t)=0 ( for i=1,2) and the periodic conditions y(x,t+T)=y(x,t), yt(x,t+T)=yt(x,t). Such a model arises from the forced vibrations of a nonhomogeneous string and the propagation of seismic waves in nonisotropic media. A main concept is the notion “weak solution” to be given in Section 2. For T is the rational multiple of π, we prove some important properties of the weak solution operator. Based on these properties, the existence and regularity of weak solutions are obtained.  相似文献   
978.
In this paper, the existence of solutions for a system of nonlinear equations is considered. n2 nonzero real solutions are obtained by using the critical point theory. Additionally, the Dirichlet boundary value problems of even order difference equations and partial difference equations are investigated.  相似文献   
979.
In this paper, using the upper-lower solution method, we investigate the properties of periodic quasisolutions for time-periodic nonquasimonotone reaction-diffusion systems, and present some existence, asymptotic behavior results for two ecological models.  相似文献   
980.
本文研究了一类中立型时滞差分方程的振动性和正解存在性,获得了该方程所有解振动的“Sharp”条件及存在正解的一个充分条件.  相似文献   
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