Smoothing properties and approximation of time derivatives for parabolic equations: constant time steps

We study smoothing properties and approximation of time derivativesfor time discretization schemes with constant time steps fora homogeneous parabolic problem formulated as an abstract initial-valueproblem in a Banach space. The time stepping schemes are basedon using rational functions r(z) e^–z which are A()-stablefor suitable [0, /2] and satisfy |r()| < 1, and the approximationsof time derivatives are based on using difference quotientsin time. Both smooth and non-smooth data error estimates ofoptimal order for the approximation of time derivatives areproved. Further, we apply the results to obtain error estimatesof time derivatives in the supremum norm for fully discretemethods based on discretizing the spatial variable by a finite-elementmethod.     

The Cauchy Problem for Certain Inhomogeneous Difference-Differential Parabolic Equations

We prove an existence and uniqueness theorem for classical solutions of the Cauchy problem for an inhomogeneous equation of parabolic type with shifted space variables.     

Single and Multi-Interval Legendre τ-Methods in Time for Parabolic Equations

In this paper, we take the parabolic equation with periodic boundary conditions as a model to present a spectral method with the Fourier approximation in spatial and single/multi-interval Legendre Petrov–Galerkin method in time. For the single interval spectral method in time, we obtain the optimal error estimate in L ²-norm. For the multi-interval spectral method in time, the L ²-optimal error estimate is valid in spatial. Numerical results show the efficiency of the methods.     

变系数时滞抛物型微分方程解的振动的充要条件

建立了一类变系数时滞抛物型微分方程解的振动的若干充要条件 .     

A New ADI Scheme for Solving Three-Dimensional Parabolic Equations with First-Order Derivatives and Variable Coefficients

An ADI scheme for solving three-dimensional parabolic equations withfirst-order derivatives and variable coefficients has been developed basedon our previous papers and the idea of the modified upwind differencescheme. This ADI scheme is second-order accurate and unconditionallystable. Further, a small parameter can be chosen which makes it suitablefor simulating fast-transient phenomena or for computations on fine spatialmeshes. The method is illustrated with numerical examples.     

一类三维拟抛物粘性扩散方程有限差分逼近的长时间行为(英文)

研究了一类带有周期边界条件的三维拟抛物粘性扩散方程有限差分解的长时间行为.证明了数值解的存在唯一性,离散系统全局吸引子的存在性,差分格式的长时间稳定性和收敛性.此外,我们给出了上半连续性.     

一类三维拟抛物粘性扩散方程有限差分逼近的长时间行为

研究了一类带有周期边界条件的三维拟抛物粘性扩散方程有限差分解的长时间行为.证明了数值解的存在唯一性,离散系统全局吸引子的存在性,差分格式的长时间稳定性和收敛性.此外,我们给出了上半连续性.     

具吸附项退化抛物方程解的大时间渐近行为

对如下形式的非线性抛物方程ut=up(uu)-uq,inQ∞=Ω×(0,∞)当p<1时,讨论了其解的大时间渐近性.     

一类拟线性退缩抛物型方程整体解的存在性与衰减估计

本文讨论了一类拟线性抛物型方程初边值问题整体解的存在性和衰减估计.所得结果改进并推广了文献[1]的相应结果.     

脉冲时滞抛物型方程解的振动性

本文研究了两类边界条件下有振动系数的脉冲时滞抛物型方程解的振动性,得到了若干解振动的判别准则。其结果即使用于有固定符号系数的方程,也显著地改进了已有的结果。     

非光滑时间分数阶齐次扩散方程的修正

当初值不光滑时,时间分数阶齐次扩散方程数值方法的精度会下降.为了得到高阶时间收敛格式,提出加权移位的Griinwald-Letnikov的修正格式,运用Lubich的修正方法,得到非光滑时间分数阶齐次扩散方程的收敛阶仍为O(k2).最后,通过数值算例验证了数值计算结果与理论计算结果一致.     

Time Discretisation of Parabolic Problems with the Variable 3-Step BDF

In this paper the stability of the 3-step backward differentiation formula (BDF) on variable grids for the numerical integration of time-dependent parabolic problems is analysed. A stability inequality with a stability constant depending in a controllable way on the mesh is obtained. In particular if the ratios r _j of adjacent mesh-sizes of the underlying grid satisfy the bound r _j r¯ < 1.199 then any mixture of the j-step BDF for j {1, 2, 3} is stable provided the number of changes between increasing and decreasing mesh-sizes is uniformly bounded. From the stability inequality error estimates can be obtained.     

超空时调和函数与一类非线性抛物方程

本文对超扩散过程定义了超空时调和函数并讨论了它们的某些性质，在此基础上建立了一类非线性抛物方程的正解与超空时调和函数之间的对应关系．     

Unique Solvability of Parabolic Equations with Almost-Periodic Coefficients in Hölder Spaces

We obtain a criterion for invertibility in Hölder spaces of linear parabolic operators of arbitrary order with any number of spatial variables and almost-periodic coefficients.     

Dependence of the Blow-up Time with Respect to Parameters for Semilinear Parabolic Equations with Nonlinear Memory

In this paper we discuss the bounds for the modulus of continuity of the blow-up time with respect to three parameters of λ, h, and p respectively for the initial boundary value problem of the semilinear parabolic equation.     

Existence and Blow-up of Solutions for a Nonlinear Parabolic System with Variable Exponents

In this paper, we study a nonlinear parabolic system with variable exponents. The existence of classical solutions to an initial and boundary value problem is obtained by a fixed point theorem of the contraction mapping, and the blow-up property of solutions in finite time is obtained with the help of the eigenfunction of the Laplace equation and a delicate estimate.     

两个带变时间步的两重网格算法的稳定性分析

对用于求解非线性发展方程的两个带变时间步的两重网格算法，对空间变量用有限元离散，对时间变量分别用一阶精度Euler显式和二阶精度半隐式差分格式离散，然后构造两重网格算法，通过深入的稳定性分析，得出本文的算法优于标准全离散有限元算法。     

一种新的快速逼近真值的程序算法──分布误差法

本文介绍一种新的逼近真值的快速程序算法及其应用。