一类三维二阶常微分方程组边值问题正解的存在性

利用Ｋｒａｓｎｏｎｅｌｓｋｉｉ不动点定理,研 究了二阶微分方程组 －ｕ″＝ａ（ｔ,ｗ）ｆ（ｕ,ｖ）, －ｖ″＝ｂ（ｔ,ｗ）ｇ（ｕ,ｖ）, －ｗ″＝ｈ（ｔ,ｕ,ｖ）, ｕ（０）＝ｕ（１）＝ｖ（０）＝ｖ（１）＝ 　　ｗ（０）＝ｗ（１）＝ { ０ 的边值问题在某些条件下正解的存 在性．     

一类退缩反应扩散方程组初边值问题解的存在性和唯一性

利用紧性理论，证明了扩散现象中出现的一类退缩抛物型方程组初边值问题解的存在性和唯一性。     

一类三阶微分方程组边值问题特殊正解的存在性

采用地面降水资料、多普勒雷达数据、探空资料等,利用自主开发的系统软件对实测资料进行增雨效果统计检验,通过目标区作业前后雷达参量的演变或目标区与对比区的回波参量的差异,来完整的分析2010年8月11日海南西部多点作业情况的催化效果。物理统计分析结果显示,催化一般在作业后半小时内起到效果并达到最强,目标区的最大强度、强回波区面积、液态水含量、回波顶高的增大率大于对比区的值,催化作业确实延长了目标云的寿命。     

一类四阶m点边值问题的正解

利用Krasnoselskii不动点定理与不动点指数理论,研究了一类四阶m点边值问题正解的存在情况,在适当的条件下,证明了该类边值问题至少存在一个正解或两个正解.     

一类偶数阶Sturm-Liouvile四点边值问题多个正解的存在性

讨论了一类偶数阶四点边值问题正解的存在性,借助Leggett-Williams不动点定理和不等式技巧,得到了该边值问题至少存在三个和任意奇数个正解的充分条件.     

带积分边界条件的奇异方程组边值问题的正解

考虑了一类具p-Laplacian算子型带积分边界条件的三点奇异方程组边值问题正解的存在性.通过使用锥上的不动点定理,在适当的条件下,建立了这类方程组边值问题存在一个或多个正解的充分条件,并给出两个例子来验证主要结果.     

一类常系数线性奇异积分方程的讨论

在“矩形”主值的基础上,获得合成公式,并利用合成公式讨论了一类相应的常系数线性奇异积分方程。     

一类ｐ Ｌａｐｌａｃｉａｎ奇异型方程组三阶三点边值问题正解的存在性

利用不动点指数定理与不等式技巧,讨论了一类ｐ Ｌａｐｌａｃｉａｎ奇异型方程组边值问题正解的存在性,建立其存在一个正解的充分条件,并对其中的一个结果给出了应用的例子．     

一类热流问题解的存在性

热敏半导体器件中电位与温度满足的方程组，是一个椭圆－抛物耦合组，并带有混合边界条件。利用不动点定理可证明该问题解的存在性。     

不同方案求解非线性化学动力学方程组的比较

在一个简化的气相化学模式的基础上,比较了Hybrid、QSSA、Sklarew三种计算方案求解非线性化学动力学方程组的差异,并引入误差分配和线性组合两种质量守恒技术,分析它们对模拟结果的影响。研究结果表明：不同方案对有机烃类浓度的计算几乎没有影响,但对其它气态物浓度有一定的影响。用QSSA和Slarew方案预测的结果更为相近,而采用Hybrid方案得到的气态物浓度的平衡时间略为提前。从计算效率来看,QSSA方案优于其它两种方案,两种质量守恒技术均能改善模拟结果。     

一类扰动时滞微分方程的多重周期解

讨论了一类扰动时滞微分方程的多重周期解的存在性问题,运用凸Hamilton系统理论和Morse指标理论得到了这类方程多重周期解的存在性。     

边界微分方程及其应用

本文讨论二维Helmholtz方程外边值问题的求解,以较为严格的方式建立了更精准的新的边界微分方程.在贴体坐标系下,Helmholtz方程可转化为非齐次Bessel方程.将Bessel方程的一般解代入Sommerfeld辐射条件可以得到等价于原Helmholtz方程的积分-微分方程,再利用分部积分消去其中积分,即可建立高频问题的边界微分方程.文中通过若干算例对新得到的边界微分方程进行了数值验证.     

一类反应扩散方程组正平衡解的存在性与唯一性

利用锥映射不动点指数计算方法,结合极值原理、解耦方法得到了一类反应扩散方程组正平衡解的存在性和唯一性.分析过程表明,对此类微分方程组的解耦方法类似于代数方程中的消元法.     

一类退化抛物型方程全局解的存在性与爆破

研究了一类具有一致Dirichlet边界条件的非线性退化抛物型方程组解的爆破和全局存在性，给出了解全局存在的一个充分必要条件。     

一类奇异二阶三点方程组正解的存在性

应用不动点理论,研究了下列奇异非线性二阶三点方程组边值问题 {u″（t）＋a（t）f（t,u,v）=0,0〈t〈1, v″（t）＋b（t）g（t,u,v）=0,0〈t〈1, u′（0）=v′（0）=0, u（1）＋αu′（η）=v（1）＋αv′（η）=0 正解的存在性,其中0〈η〈1,并且允许口a（t）、b（t）在t=0和t=1处奇异。     

A Homogeneous Langevin Equation Model, Part ii: Simulation of Dispersion in the Convective Boundary Layer

We present a Lagrangian stochastic model of vertical dispersion in the convective boundary layer (CBL). This model is based on a generalized Langevin equation that uses the simplifying assumption that the skewed vertical velocity probability distribution is spatially homogeneous. This approach has been shown to account for two key properties of CBL turbulence associated with large-scale coherent turbulent structures: skewed vertical velocity distributions and long velocity correlation time. A 'linear-skewed' form of the generalized Langevin equation is used, which has a linear (in velocity) deterministic acceleration and a skewed random acceleration. 'Reflection' boundary conditions for selecting a new velocity for a particle that encounters a boundary were investigated, including alternatives to the standard assumption that the magnitudes of the particle incident and reflected velocities are positively correlated. Model simulations were tested using cases for which exact, analytic statistical properties of particle velocity and position are known, i.e., well-mixed spatial and velocity distributions. Simulations of laboratory experiments of CBL dispersion show that (1) the homogeneous linear-skewed Langevin equation model (as well as an alternative 'nonlinear-Gaussian' Langevin equation model) can simulate the important aspects of dispersion in the CBL, and (2) a negatively-correlated-speed reflection boundary condition simulates the observed dispersion of material near the surface in the CBL significantly better than alternative reflection boundary conditions. The homogeneous linear-skewed Langevin equation model has the advantage that it is computationally more efficient than the homogeneous nonlinear-Gaussian Langevin equation model, and considerably more efficient than inhomogeneous Langevin equation models.     

非线性平流方程计算稳定性对初值的依赖性研究

对一维平流方程向前差格式的一个计算不稳定特例进行了讨论，给出了四个命题，并得出结论：在一定的条件下，可以对初值稍加改变，使其在x轴一侧分布而达到计算稳定，从而改进并修正了已有的相关结论。     

On the Possible Impact of a Following-Swell on the Atmospheric Boundary Layer

A simple model of the atmospheric boundary layer over the ocean where the swell impact on the atmosphere is explicitly accounted for is suggested. The model is based on Ekman’s equations, where the stress in the wave boundary layer is split into two parts: the turbulent and wave-induced stress. The turbulent stress is parameterized traditionally via the eddy viscosity proportional to the generalized mixing length. The wave-induced stress directed upward (from swell to the atmosphere) is parameterized using the formalism of the wind-over-waves coupling theory. The model can be seen as an extension of the model by Kudryavtsev and Makin (J Phys Oceanogr 34:934–949, 2004) to the scale of the entire atmospheric boundary layer by including the Coriolis force into the momentum conservation equation and generalizing the definition of the mixing length. The regime of low winds for swell propagating along the wind direction is studied. It is shown that the impact of swell on the atmosphere is governed mainly by the swell parameter—the coupling parameter that is the product of the swell steepness and the growth rate coefficient. When the coupling parameter drops below − 1 the impact of swell becomes significant and affects the entire atmospheric boundary layer. The turbulent stress is enhanced near the surface as compared to the no-swell case, and becomes negative above the height of the inner region. The wind profile is characterized by a positive gradient near the surface and a negative gradient above the height of the inner region forming a characteristic bump at the height of the inner region. Results of the model agree at least qualitatively with observations performed in the atmosphere in presence of swell.