Local Classical Solution of Muskat Free Boundary Problem

In this paper we consider the two-dimensional Muskat free boundary problem: Δu_i(x,t) = 0 in space-time domain Q_i (i = 1,2), here tis a parameter. The unknown surface Γ_pT (free boundary) is tltc common part of the boundaries of Q_1 and Q_2. The free boundary conditions are u_1(x,t) = u_2(x,t) and -k_1\frac{∂u_1}{∂n} = -k_2\frac{∂u_2}{∂n} = V_n. If the initial normal velocity of the free boundary is positive, we shall prove the existence of classical solution locally in time and uniqueness by making use of Newton's iteration method.     

双层浅水波模型柯西问题的经典解

主要研究浅水理论中双层浅水波模型柯西问题的经典解.在适当的初值条件下,得到整体经典解存在唯一性的充要条件.同时对单层浅水波模型也得到相应结果.     

Life-span of Classical Solutions to Nonlinear Wave Equations in Two-space-dimensions II

In two-space-dimensional case we get the sharp lower bound of the life-span of classical solutions to the Cauchy problem with small initial data for fully nonlinear wave equations of the form ◻u = F (u, Du, D_zDu) in which F(\hat{λ}) = O(|\hat{λ}|^{1+α}) with α = 2 in a neighbourhood of \hat{λ} = 0. The cases α = 1 and α ≥ 3 have been considered respectively in [1] and [2].     

非线性波动方程经典解的整体存在性

该文证明了波动方程uu－△u＝F（u，Du）的Cauchy问题整体经典解的存在性唯一性，并对方程中出现的每项u，Du，D2u的某种范数均得到了与齐次方程相同的衰减估计，其结果补充和丰富了[4]中F不显含u时的结果．     

相同装卸工情况下装卸工问题的最优解

装卸工问题是一个新的NP困难的组合最优化问题,寻找其性能优良的近似算法是有重要的理论意义和实用价值的.相同装卸工情况下装卸工问题的系数矩阵是全么模矩阵,利用全么模矩阵的性质可以证明这种情况下的装卸工问题是多项式可解的.然而用全么模阵的性质还不能得到解的表达式.对这种情况下一辆货车的装卸工问题,用对偶单纯形法可得到最优解和最优值的解析表达式,从而可以把这个可解问题的最优值作为一般装卸工问题的近似值.这对于分析近似算法的性态是非常重要的.     

Global Classical Solutions to Partially Dissipative Quasilinear Hyperbolic Systems

The author considers the Cauchy problem for quasilinear inhomogeneous hyperbolic systems. Under the assumption that the system is weakly dissipative, Hanouzet and Natalini established the global existence of smooth solutions for small initial data (in Arch. Rational Mech. Anal., Vol. 169, 2003, pp. 89–117). The aim of this paper is to give a completely different proof of this result with slightly different assumptions.     

一类周期自由边界问题解的渐近性态

本文证明了化学反应扩散过程中的一类周期自由边界问题古典解的存在唯一性，并且讨论了潜热L→0时周期Stefan问题古典解的渐近性态及误差估计．     

初值的导数具有紧支集的对角形双曲组Cauchy问题经典解的整体存在唯一性

本文研究了初值导数具有紧支集的对角形严格双曲组Cauchy问题在t>0上的经典解的整体存在唯一性,以及在最大特征的决定区域内的较一般的非严格双曲组的初值是在x≥0半轴上给定的,并且初值具有紧支集的Cauchy问题的经典解的整体存在唯一性.文中主要使用了特征线方法和解的一致先验估计方法.     

一维Navier-Stokes方程组整体经典解

本文作者考虑了一维Navier-Stokes方程组Cauchy问题,得到了其经典解的整体光滑可解性。     

Existence of Classical Solution of a Quasilinear Stefan-Signorini Problem

In this paper, we consider an one-phase quasilinear Stefan-Signorini problem. In [1] X. Liu has proved the existence and the uniqueness of this problem by the traditional penalty method (see [3] and [4]). Here we use the Mixed Scheme in [2] which is more suitable to the Stefan-Signorini problem and obtain more natural existence results.     

不要把问题解决教学课上成问题解答介绍课——兼评分部积分法的两种不同的教学方法

结合数学分析中分部积分法这一内容的两种不同的教学方法,论述了在问题解决教学中切忌把问题解决教学课上成问题解答介绍课.     

一维磁流体力学方程组经典解的生命区间

考虑具耗散项的一维磁流体力学方程组Cauchy问题．对于非耗散情形证明了如果初始能量和磁场强度弱于声波的能量,则Cauchy问题的光滑解在有限时间内破裂;对于耗散情形,如果初始能量、磁场强度和耗散强度弱于声波的能量,则Cauchy问题的光滑解在有限时间内破裂,而且给出了生命区间估计．     

一阶非齐次拟线性双曲组的柯西问题整体经典解的存在性

本文考察了弱线性退化的一阶非齐次拟线性严格双曲组具有小初值的柯西问题．在非齐次项满足匹配条件的假设下,给出了精细的波的分解公式,利用这些公式,证明了整体C1解的存在唯一性和稳定性．     

系数变号时经典Emden方程的两点边值问题的正解

建立了边值问题w″ k(t)w^α=0,w(0)=w(1)=0的一个正解存在定理,其中允许k(t)的[0,1]上改变符号。     

一个具有动态条件的Verigin问题

本文考虑了一个具有动态条件的Verigin问题,得到了这个问题关于时间的局部古典解的存在唯一性.     

具有Kinetic的Muskat问题古典解

考虑了具有Kinetic的多维Muskat问题，并得到了这个问题局部古典解存在唯一性。     

Local Classical Solutions to the Equations of Relativistic Hydrodynamics

In this paper, we prove that the convexity of the negative thermodynamical entropy of the equations of relativistic hydrodynamics for ideal gas keeps its invariance under the Lorentz transformation if and only if the local sound speed is less than the light speed in vacuum. Then a symmetric form for the equations of relativistic hydrodynamics is presented and the local classical solution is obtained. Based on this, we prove that the nonrelativistic limit of the local classical solution to the relativistic hydrodynamics equations for relativistic gas is the local classical solution of the Euler equations for polytropic gas.     

拟线性双曲组在半有界初始轴上的柯西问题整体经典解的渐近性态

In this paper we study the asymptotic behavior of global classical solutions to the Cauchy problem with initial data given on a semi-bounded axis for quasilinear hyperbolic systems. Based on the existence result on the global classical solution, we prove that, when t tends to the infinity, the solution approaches a combination of C1 travelling wave solutions with the algebraic rate （1 ＋ t）^-u, provided that the initial data decay with the rate （1 ＋ x）^-（l＋u） （resp. （1 - x）^-（1＋u）） as x tends to ＋∞ （resp. -∞）, where u is a positive constant.     

关于等周问题级数解法的一些改进

对苏步青教授在文[1]中介绍的改良的Hurwitz方法再作一些改进,先对Wirtinger引理进行推广,再用推广后的Wirtinger不等式很自然而简洁地推出了等周不等式.     

Global Classical Solutions to the Equations of Two-dimensional MHD Transverse Flow

A new method for constructing the symmetric form for the hyperbolic systems is introduced. Then a new symmetric form of the equations of MHD transverse flow is constructed by adding an additional equation. With this new form, we obtain the local existence of smooth solution including the case that the initial density may tend to the vacuum state at infinity. Furthermore, the uniformly a priori estimation for the classical solutions is established and the global smooth solutions for a kind of initial data are obtained.