具浓度相关迁移率的粘性Cahn-Hilliard方程

This paper is devoted to viscous Cahn-Hiliiard equation with concentration dependent mobility. Some results on the existence, uniqueness and large time behavior are established.     

具浓度相关迁移率的对流扩散Cahn-Hilliard方程

In this paper, we study the global existence of classical solutions for the convective-diffusive Cahn-Hilliard equation with concentration dependent mobility. Based on the Schauder type estimates, we establish the global existence of classicalsolutions.     

具位势项的快扩散方程的第二临界指标

This paper considers a fast diffusion equation with potential ut= um V (x)um+upin Rn×(0,T), where 1 2αm+n< m ≤ 1, p > 1, n ≥ 2, V (x) ～ω|x|2with ω≥ 0 as |x| →∞,and α is the positive root of αm(αm + n 2) ω = 0. The critical Fujita exponent was determined as pc= m +2αm+nin a previous paper of the authors. In the present paper,we establish the second critical exponent to identify the global and non-global solutions in their co-existence parameter region p > pcvia the critical decay rates of the initial data.With u0(x) ～ |x| aas |x| →∞, it is shown that the second critical exponent a =2p m,independent of the potential parameter ω, is quite different from the situation for the critical exponent pc.     

具有浓度迁移率和对数势能的粘性Cahn-Hilliard方程的有限元算法

对于具有浓度迁移率和对数势能的粘性Cahn-Hilliard方程,在空间上采用混合有限元方法进行了离散,在时间上采用Crank-Nicolson格式进行了离散.首先,证明了该全离散格式的无条件能量稳定性.其次,详细地证明了H~1空间上的最优误差估计.最后,通过一些算例对所提格式的有效性进行了验证.结果表明,理论分析与数值实验相一致.     

紧致黎曼流形上一类非线性热方程的梯度估计

In this paper,we study gradient estimates for the nonlinear heat equation ut-△u =au log u,on compact Riemannian manifold with or without boundary.We get a Hamilton type gradient estimate for the positi...     

非线性Cahn-Hilliard方程的拟谱算法

本文对非线性Cahn-Hilliard方程构造了拟谱格式,证明了该格式的收敛性和稳定性,给出了数值例子.     

具浓度相关迁移矩阵的Cahn-Hilliard方程组

人们熟悉的Cahn－Hilliard方程曾作为研究两相混合物间相交的模型提出．若该混合物由m＋1种物质组成,则可由Cahn－Hilliard方程导出由m个方程组成的偏微分方程组．在适当的假设下,本文证明自然的和质量守恒边界条件唯一确定该混合物中各种物质的比例.     

Cahn-Hilliard方程非条件能量稳定二阶方法的稳定性和收敛性分析

在这项工作中,我们构建了一种非条件能量稳定的高效不变能量四分法(IEQ)来求解Cahn-Hilliard方程.所构建的数值格式是线性的、具有二阶时间精度和非条件能量稳定性.我们仔细分析了数值格式的唯一可解性、稳定性和误差估计.结果表明,所构建的格式满足唯一可解性、非条件能量稳定性和时间方向的二阶收敛性.通过大量的二维和三维数值实验,我们进一步验证了所提出格式的收敛阶、非条件能量稳定性和有效性.     

具有惯性项和阻尼项的Cahn-Hilliard方程的整体吸引子

本文研究具有惯性项和阻尼项的亚三次非线性Cahn-Hilliard方程的初边值问题.在非线性弱正则的条件下,我们建立弱解的适定性,而不考虑非线性项的一阶导数的下界条件.接着利用弱解的渐近紧和能量解的严格Lyapunov函数的存在性,证明在空间(H~2(?)∩H_0~1(?))×L~2(?)上存在整体吸引子.     

二维Cahn-Hilliard方程半隐的预估-校正谱逼近(英文)

针对二维Cahn-Hilliard方程的初边值问题提出了一个便于计算的、半隐的预估-校正谱格式.通过引入两个三线性泛函,克服了非线性项所带来的困难,并用能量方法严格证明了数值解在时间方向具有二阶精度,而在空间方向具有谱精度.     

Two Dimensional Cahn-Hilliard Equation with Concentration Dependent Mobility and Gradient Dependent Potential

In this paper we consider the initial boundary value problem of Cahn-Hilliard equation with concentration dependent mobility and gradient dependent potential. By the L~P type estimates and the theory of Morrey spaces,we prove the Holder continuity of the solutions.Then we obtain the existence of global classical solutions.The present work can be viewed as an extension to the previous work on the Cahn-Hilliard equation with concentration dependent mobility and potential.     

On the convective Cahn-Hilliard equation with degenerate mobility

In this paper, we study the existence of weak solutions for the convective Cahn-Hilliard equation with degenerate mobility. Based on the Schauder type estimates, we establish the global existence of classical solutions for regularized problems. After establishing some necessary uniform estimates on the approximate solutions, we prove the existence of weak solutions. The nonnegativity and the finite speed of propagation of perturbations of solutions are also discussed.     

Finite Speed of Propagation of Perturbations for the Cahn-Hilliard Equation with Degenerate Mobility

This paper is devoted to the Cabn-Hilliard equation with degenerate mobility in two spatial variables with a typical case modelling thin viscous film spreading over a solid surface. We establish tbe existence of radial symmetric solutions with the property of finite speed of perturbations.     

Non-blow-up phenomenon for the Cahn-Hilliard equation with non-constant mobility

In this paper we prove that the finite time blow-up phenomenon might not occur for the Cahn-Hilliard equation with non-constant mobility and cubic nonlinearity, which is quite different from the case of constant mobility. We reveal such a phenomenon under some structure condition on the mobility.     

A CAHN-HILLIARD TYPE EQUATION WITH GRADIENT DEPENDENT POTENTIAL

We investigate a Cahn-Hilliard type equation with gradient dependent potential. After establishing the existence and uniqueness, we pay our attention mainly to the regularity of weak solutions by means of the energy estimates and the theory of Campanato Spaces.     

具有对数势能的Cahn-Hilliard方程的有限元算法

本文我们提出了具有对数势能的Cahn-Hilliard方程,在空间上采用混合有限元方法进行离散,时间上采用Crank-Nicolson格式.运用正则性,将对数势能函数F(u)的定义域的范围由(-1,1)扩展到(-∞,∞).证明该方法是能量耗散的,并计算误差估计,最后通过数值算例对理论部分进行验证.结果表明,理论与数值算...     

A Note on the Viscous Cahn-Hilliard Equation

In this note, we study the global existence of classical solutions for the viscous Cahn-Hilliard equation with spatial dimension n ≤ 5. Based on the Schauder type estimates and energy estimates, we establish the global existence of classical solutions.