带有扰动算子和误差数据的不适定方程的A-光滑正则化

1　Ｉｎｔｒｏｄｕｃｔｉｏｎ　ＬｅｔＸ ,ＹｂｅｔｗｏＨｉｌｂｅｒｔｓｐａｃｅｓａｎｄｌｅｔＡ∈Ｂ(Ｘ ,Ｙ) ,ｉ .ｅ .,ａｂｏｕｎｄｅｄｌｉｎｅａｒｏｐｅｒａｔｏｒ .ＣｏｎｓｉｄｅｒｔｈｅｏｐｅｒａｔｏｒｅｑｕａｔｉｏｎＡｘ =ｙ (1.1)ＩｆＲ(Ａ) ,ｉ .ｅ .,ｔｈｅｒａｎｇｅｏｆＡ ,ｉｓｎｏｎ ｃｌｏｓｅｄｉｎＹ ,Ｅｑ .(1.1)ｉｓｉｌｌ ｐｏｓｅｄ[1] .Ｍａｎｙｉｍｐｏｒｔａｎｔｐｒｏｂｌｅｍｓｉｎａｐｐｌｉｅｄｓｃｉｅｎｃｅｓ ,ｅｓｐｅｃｉａｌｌｙｉｎｖｅｒｓｅｐｒｏｂｌｅｍｓ ,ｒｅｓｕｌｔｉｎｔｈｉｓｋｉ…     

球面系方程及其应用

给出了五类球面系方程,并例说了球面系方程在计算、证明等中的应用。     

一类四阶非线性波动方程整体解的存在性

借助线性问题的衰减估计，在一适当的Banach空间，利用整体迭代法证明了一类非线性四阶波动方程Cauchy问题整体解的存在性     

洛仑兹力公式的相对论协变性的简化证明

讨论了带电粒子在电磁场中运动方程的协变性,给出了洛仑兹力公式是协变式的一种简化证明,最后对洛仑兹力公式的相对论协变性做一些补充说明,明确了洛仑兹力概念的正确界定.     

如何理解物理化学中热力学函数之间的关系

通过观察圆柱体几何性质间的关系和几何性质的变化对其它性质的影响，来理解物理化学中热力学函数间的关系和对应系数关系式、马克斯韦关系式里的热力学函数是如何变化的．     

Simple shear endochronic eqiations for finite plastic deformation

The endochronic equations proposed by Valanis (1980) were extended to a finite deformation range. Jaumann's rate,Fu's rate and Wu's rate were incorporated into the endochronic equations to analyze simple shear finite deformation. Incremental equations and numerical solutions are deduced for three endochronic objective models. The results show that an oscillatory shear stress response to a monotonically increasing shear strain occurs when the Jaumann's rate objective model is employed for endochronic materials. The oscillatory response is dependent on the adopted objective rate. Compared with the Jaumann's rate, the Fu's rate and the Wu's rate satisfy the restrictions to elastic-plastic constitutive relations and are in agreement with the experimental results.     

Non-formation of vacuum states for Navier-Stokes equations with density-dependent viscosity

We consider the Cauchy problem, free boundary problem and piston problem for one-dimensional compressible Navier-Stokes equations with density-dependent viscosity. Using the reduction to absurdity method, we prove that the weak solutions to these systems do not exhibit vacuum states, provided that no vacuum states are present initially. The essential re- quirements on the solutions are that the mass and energy of the fluid are locally integrable at each time, and the Lloc1-norm of the velocity gradient is locally integrable in time.     

一类二阶非线性脉冲常微分方程解的振动性

讨论了二阶非线性脉冲常微分方程的振动性，得到了该方程所有解振动的充分条件。     

不可压磁流体方程在柱坐标下的表示及其基本能量估计

在考虑方程解的适定性时,解有有限能量总是一个最基本要求。因此,对方程做基本能量估计是非常有必要的,也是考虑解的适定性的前提。本文给出了磁流体力学方程在柱对称条件下的解的基本能量估计,这为后续的解的存在唯一性,正则性等,提供了一个保障。首先运用微积分的知识,将直角坐标系下的梯度算子和拉普拉斯算子换算成柱坐标系下的情形,进而求得柱坐标系下的磁流体力学方程表达式,而后求该方程在无旋情形(所有变量关于角变量是固定的)的基本能量估计。     

求解非线性微分方程精确行波解的代数法

给出了求解非线性微分方程精确行波解的代教法,利用此方法获得了非线性微分方程若干形式的精确行波解,并在计算机代数系统REDUCE上得以实现．