Almost automorphic solutions for semilinear boundary differential equations

In this work, we use the extrapolation methods to study the existence and uniqueness of almost automorphic solutions to the semilinear boundary differential equation

where generates a hyperbolic -semigroup on a Banach space and are almost automorphic functions which take values in and a ``boundary space' , respectively. These equations are an abstract formulation of partial differential equations with semilinear terms at the boundary, such as population equations, retarded differential equations and boundary control systems. An application to retarded differential equations is given.

     

Banach空间一阶非线性脉冲微分方程周期边值问题的解

本文通过建立Ｂａｎａｃｈ空间一阶非线性脉冲微分一积分方程周期边值问题新的比较定理,给出了其最大解和最小解的存在性。     

半正二阶三点边值问题的解和正解

考察了非线性二阶三点边值问题的n个解和正解的存在性,其中允许非线性项有一个负的下界并且n是一个任意的自然数．主要结论表明该问题可以具有n个解或者正解,只要非线性项在某些有界集上的“高度”是适当的．     

带广义边界条件的四阶抛物型方程的混合间断时空有限元法

构造具有广义边界条件的四阶线性抛物型方程的混合间断时空有限元格式,利用混合有限元方法将高阶方程降阶,利用空间连续而时间允许间断的时空有限元方法离散方程,证明了离散解的存在唯一性,稳定性和收敛性,并给出数值算例验证了方法的有效性.     

干扰剪切流动(ISF)和边界层流动及ISF理论在计算流体力学(CFD)中的应用

简述作者提出的干扰剪切流动(ISF)理论、近壁复杂ISF理论、推论和它们在CFD中的应用.ISF是小黏性流体运动中普遍存在的一种基本流动,如驻点流、近壁黏性-无黏干扰流动,干扰可忽略时ISF的黏性部分为熟知的边界层流动.ISF理论揭示了高$Re$数流动计算的最佳坐标系和最佳网格生成.由近壁复杂ISF理论与流体运动方程组及流速在壁面无滑移条件相结合导出一组壁面相容(SC)判据,该判据提供了利用CFD仿真结果判断CFD仿真可信度的理论途径、并为近壁网格、算法和边界处理的改进和三者的更好协调、为湍流模型的评估、改进和发展提供了一种理论途径.      

Regularity of CR maps between convex hypersurfaces of finite type

We study rigidity and regularity properties of CR maps between smooth convex hypersurfaces of finite type in

     

Convergence and stability of extended block boundary value methods for Volterra delay integro-differential equations

In this paper, we construct a class of extended block boundary value methods (B₂VMs) for Volterra delay integro-differential equations and analyze the convergence and stability of the methods. It is proven under the classical Lipschitz condition that an extended B₂VM is convergent of order p if the underlying boundary value methods (BVM) has consistent order p. The analysis shows that a B₂VM extended by an A-stable BVM can preserve the delay-independent stability of the underlying linear systems. Moreover, under some suitable conditions, the extended B₂VMs can also keep the delay-dependent stability of the underlying linear systems. In the end, we test the computational effectiveness by applying the introduced methods to the Volterra delay dynamical model of two interacting species, where the theoretical precision of the methods is further verified.     

含有一阶导数的四阶边值问题正解的存在性

研究了含有一阶导数的四阶边值问题,利用度理论构造出的一个新的不动点定理,由Green函数的性质,给出了一类含有导数的四阶边值问题正解存在的充分条件,得到了边值问题正解存在的一些新结果.     

一类非线性椭圆型方程的奇异边值问题

本文研究一类在球内的非线性椭圆奇异边值问题的正解的存在性,推广了Ｈ．Ｕｓａｍｉ１９８９年所得到的部分结果