中立型脉冲发展方程解的存在性和唯一性

本文研究了一类非线性中立型脉冲发展方程解的存在性和唯一性的问题.利用迭代分析方法结合半群理论的知识,得到了其解的表达式,并构造解的迭代序列,同时证明了其解的存在性和唯一性.通过研究发现其解的存在性和唯一性与脉冲时滞条件密不可分,利用迭代分析法求解此类问题具有一定的优越性.     

一类线性积分方程解的存在唯一性

在这篇文章内我们证明了一类线性积分方程存在唯一解．并给出解的表示式．它以Ｆｒｅｄｈｏｌｍ方程和Ｖｏｌｔｅｒｒａ方程为特殊情形．     

EXISTENCE AND UNIQUENESS OF THE SOLUTION TO THE VISCOELASTIC EQUATIONS FOR KOITER SHELLS

In this paper,we consider the linearly viscoelastic equations for Koiter shells. Also,we prove the existence and uniqueness of the solution by Galerkin method.     

ON THE EXISTENCE AND UNIQUENESS OF THE SOLUTION TO THE NAVIER－STOKES EQUATIONS

ＯＮＴＨＥＥＸＩＳＴＥＮＣＥＡＮＤＵＮＩＱＵＥＮＥＳＳＯＦＴＨＥＳＯＬＵＴＩＯＮＴＯＴＨＥＮＡＶＩＥＲ－ＳＴＯＫＥＳＥＱＵＡＴＩＯＮＳＴａｎｇＸｉａｎｊｉａｎｇ（Ｄｅｐｔ．ｏｆＭａｔｈ．，Ｓｉｃｈｕａｎｕｎｉｖｅｒｓｉｔｙ，Ｃｈｅｎｇｄｕ６１００６４...     

THE EXISTENCE OF GLOBAL SOLUTION AND THE BLOWUP PROBLEM FOR SOME p-LAPLACE HEAT EQUATIONS

This article consider, for the following heat equation ut/|x|s-△pu=uq,(x,t)∈Ω×(0,T), u(x,t)=0,(x,t)∈(?)Ω×(0,T), u(x,0)=u0(x),u0(x)≥0,u0(x)(?)0 the existence of global solution under some conditions and give two sufficient conditions for the blow up of local solution in finite time, whereΩis a smooth bounded domain in RN(N>p),0∈Ω,△pu=div(|▽u|p-2▽u),0≤s≤2,p≥2,p-1相似文献   

带阻尼项的Euler方程组初边值问题的整体解

本文研究了一维带阻尼项的Euler方程组初边值问题的齐次Dirichlet边值情形.当初值在平衡解附近小扰动时,本文得到了时间整体解的存在唯一性,而且当时间趋于无穷时,此解趋于平衡解.     

随机发展方程适度解的整体存在唯一性

本文考虑了如下Ｈｉｌｂｅｒｔ空间中半线性随机发展方程（１）的Ｃａｕｃｈｙ问题，在两组不同的条件下，分别得到了该问题的适度解的整体存在唯一性。     

奇异Hamilton-Jacobi-Bellman方程粘性解的存在唯一性

研究系数在边界点有奇性的一类Hamilt on- Jacobi- Bellman (HJB)方程的粘性解的存在唯一性问题及解的渐近估计,这类问题包括波动系数振荡或爆破的情况.奇异HJB方程在随机最优控制和金融数学等许多领域都有重要的应用,包括金融数学中的随机利率模型.应用粘性上下解理论建立了一类奇异HJB方程的比较原理,给出了粘性解存在唯一性的条件.     

GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR FOR THE 3D COMPRESSIBLE NON–ISENTROPIC EULER EQUATIONS WITH DAMPING

We investigate the global existence and asymptotic behavior of classical solutions for the 3D compressible non-isentropic damped Euler equations on a periodic domain. The global existence and uniqueness of classical solutions are obtained when the initial data is near an equilibrium. Furthermore, the exponential convergence rates of the pressure and velocity are also proved by delicate energy methods.     

EXISTENCE AND UNIQUENESS OF GLOBAL SOLUTIONS OF THE MODIFIED KS-CGL EQUATIONS FOR FLAMES GOVERNED BY A SEQUENTIAL REACTION

In this paper, we are concerned with the existence and uniqueness of global solutions of the modified KS-CGL equations for flames governed by a sequential reaction, where the term |P|~2P is replaced with the generalized form |P|~(2σ)P,see [18]. The main novelty compared with [18] in this paper is to control the norms of the first order of the solutions and extend the global well-posedness to three dimensional space.     

一类非经典扩散方程整体解的存在唯一性及长时间行为

本文讨论非经典扩散方程第一初边值问题整体解的存在唯一性及长时间行为，建立了一系列新的结果，较好地改进许多已有的结论．     

Banach空间中n阶非线性微分积分方程初值问题解的存在与唯一性

用压缩映象原理研究Banach空间中定义在无界域上的n阶非线性Volterra型微分积分方程初值问题,获得了解的存在与唯一性及其迭代逼近新结果。     

一类半线性椭圆方程解的存在性

本文研究了一类具有临界增长的半线性椭圆型方程.采用最近A.Ambrosetti所提出的扰动方法研究这类问题,得到这类问题的解的存在性.与通常所用的临界点理论方法相比较,本文解的存在性在较弱条件下可得.     

EXISTENCE AND UNIQUENESS OF ENTROPY SOLUTION TO PRESSURELESS EULER SYSTEM WITH A FLOCKING DISSIPATION

We study the existence and uniqueness problem for the nonhomogeneous pressureless Euler system with the initial density being a Radon measure. Our uniqueness result is obtained in the same space as the existence theorem. Besides, by counterexample we prove that Huang-Wang's energy condition is also necessary for our nonhomogeneous system.     

EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR DELAY STOCHASTIC EVOLUTION EQUATIONS

Some results on the existence and uniqueness of solutions for stochastic evolution equations containing some hereditary characteristics are proved. In fact, our theory is developed from a variational point of view and in a general functional setting which permit us to deal with several kinds of delay terms in a unified formulation.     

一类具积分项非线性梁方程整体解的存在性

讨论了一类在轴向载荷作用下,有限长粘弹性梁的非线性振动问题,用Galerkin方法证明了问题的整体强解和整体经典解的存在性.     

拉单晶问题数学模型弱解的存在性和唯一性

本文考虑楔形区域Ｇ０Ｔ上的二相自由边界问题：其中ａ，ｂ，ｂ１，νｐ，ｈ２为正常数。本文在适当的假设之下，证明了上述定解问题弱解的存在性和唯一性。     

非局部非线性发展方程解的存在性与唯一性

本文利用Ｂａｎａｃｈ不动点定理证明一类非线性发展方程的非局部Ｃａｕｃｈｙ问题解的存在性与唯一性，及其对非局部拟线性抛物方程的应用。