A REMARK ON HOFER-ZEHNDER SYMPLECTIC CAPACITY IN SYMPLECTIC MANIFOLDS M×R~(2n)

ＡＲＥＭＡＲＫＯＮＨＯＦＥＲＺＥＨＮＤＥＲＳＹＭＰＬＥＣＴＩＣＣＡＰＡＣＩＴＹＩＮＳＹＭＰＬＥＣＴＩＣＭＡＮＩＦＯＬＤＳＭ×Ｒ２ｎＭＡＲＥＮＹＩＡｂｓｔｒａｃｔＴｈｅａｕｔｈｏｒｓｔｕｄｉｅｓｔｈｅＨｏｆｅｒＺｅｈｎｄｅｒｃａｐａｃｉｔｙａ...     

ON THE UPPER ESTIMATES OF FUNDAMENTAL SOLUTIONS OF PARABOLIC EQUATIONS ON RIEMANNIAN MANIFOLDS

ＯＮＴＨＥＵＰＰＥＲＥＳＴＩＭＡＴＥＳＯＦＦＵＮＤＡＭＥＮＴＡＬＳＯＬＵＴＩＯＮＳＯＦＰＡＲＡＢＯＬＩＣＥＱＵＡＴＩＯＮＳＯＮＲＩＥＭＡＮＮＩＡＮＭＡＮＩＦＯＬＤＳ￥ＬＩＪＩＡＹＵ；ＳＨＡＯＸＩＮ（ＤｅｐａｒｔｍｅｌｌｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ａ...     

一类非线性渗流方程Cauchy问题弱解的存在唯一性

讨论具强非线性源和对流项的一般渗流方程以Ｒ＾Ｎ中某一Ｒａｄｏｎ测度为初始迹的Ｃａｕｃｈｙ问题弱解的存在唯一性。     

渗流方程差分解的收敛性

渗流方程是拟线性退化抛物型方程。[1—4]讨论了弱解的存在唯一性问题。由于非线性扩散系数有零点,其解可以不光滑。在[5,6]中研究了渗流方程 u_t=(u~m)_(xx),m>1的差分方法问题,对光滑区和弱间断点给以分别处理。渗流方程的解是连续的,但在有些点上导数不存在。因此,不能用Taylor展开估计截断误差的方法证明差分解的收敛性。     

A HARNACK TYPE INEQUALITY FOR SOME CONFORMALLY INVARIANT EQUATIONS ON HALF EUCLIDEAN SPACE

We establish a Harnack type inequality on half Euclidean space for general conformally invariant fully nonlinear elliptic equations of second order.     

一般非线性渗流方程正性的扩展

本文研究一般非线性渗流方程解的一种性态.利用De Giorgi方法与BCP估计相结合,得到了一般非线性渗流方程正性的扩展性质,推广了非线性渗流方程的结果.     

LARGE TIME BEHAVIOR OF SOLUTIONS TO NEWTONIAN FILTRATION EQUATIONS WITH SOURCES

This article is concerned with large time behavior of solutions to the Neumann or Dirichlet problem for a class of Newtonian filtration equations |x|λ+k ■u■ t = div(|x|k▽um) + |x|λ+kupwith 0 m 1, p 1, λ≥ 0, k ∈ R. An interesting phenomenon is that there exist two thresholds k∞ and k1 for the exponent k, such that the critical Fujita exponent pc for p exists and is finite if k ∈ (k∞, k1), otherwise, pc is infinite or does not exist.     

DENSITY ESTIMATES FOR SOLUTIONS OF STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS

In this article, we investigate the density of the solution to a class of stochastic functional differential equations by means of Malliavin calculus. Our aim is to provide upper and lower Gaussian estimates for the density.     

对流反应扩散方程的稳定化时间间断时空有限元解的误差估计

在流线迎风Petrov-Galerkin（SUPG）稳定化有限元数值格式的基础上,结合时间方向的变分离散,构造对流反应扩散方程的稳定化时间间断时空有限元格式.该类格式在工程上有一些数值模拟应用,但相关文献没有看到类似数值格式的理论证明.本文以Radau点为节点,构造时间方向的Lagrange插值多项式,证明了稳定化有限元解的稳定性,时间最大模、空间L²（Ω）-模误差估计.文中利用插值多项式和有限元方法相结合的技巧,解耦时空变量,去掉了时空网格的限制条件,提供了时间间断稳定化时空有限元方法的理论证明思路,克服了因时空变量统一导致的实际计算时的复杂性.     

HOLDER ESTIMATES FOR SOLUTIONS OF UNIFORMLY DEGENERATE QUASILINEAR PARABOLIC EQUATIONS

In this paper the author discusses the quasilinear parabolic equation $$\[\frac{{\partial u}}{{\partial t}} = \frac{\partial }{{\partial {x_i}}}[{a_{ij}}(x,t,u)\frac{{\partial u}}{{\partial {x_j}}}] + {b_i}(x,t,u)\frac{{\partial u}}{{\partial {x_i}}} + c(x,t,u)\]$$ Which is uniformly degenerate at $\[u = 0\]$. Let $\[u(x,t)\]$ be a classical solution of the equation satisfying $\[0 < u(x,t) \le M\]$. Under some assumptions the author establishes the interior estimations of Holder coefficient of the solution for the equation and the global estimations for Cauchy problems and the first boundary value problems, where Holder ooeffioients and exponents are independent of the lower positive bound of $\[u(x,t)\]$.     

RN上的临界非齐次多重调和方程的多解存在性

讨论了 RN上带非负扰动的临界非齐次多重调和方程的多解存在性 .首先由泛函弱连续性方法获得方程的第一个解 ,再由山路引理获得方程的第二个解 .本文的这种求解方法和这些结果不仅适用于 RN 上的二阶椭圆方程 ,而且也适用于尚未解决的 RN 上的双调和方程     

SOLITARY WAVE AND PERIODIC WAVE SOLUTIONS FOR THE NON-NEWTONIAN FILTRATION EQUATIONS WITH NONLINEAR SOURCES AND A TIME-VARYING DELAY

This paper is concerned with the non-Newtonian filtration equations with nonlinear sources and a time-varying delay. By an extension of Mawhin's continuation theorem and some analysis methods,several sufficient conditions ensuring the existence of solitary wave and periodic wave solutions are obtained. Some corresponding results in the literature are improved and extended. An example is given to illustrate the effectiveness of our results.     

多孔介质方程在一般几何流演化下的梯度估计

本文研究了多孔介质方程在一般几何流下的梯度估计.通过Aroson和Bénilan对多孔介质方程的研究结果以及运用Li-Yau梯度估计的方法,获得了对多孔介质方程的正解对于Laplace算子以及drifing Laplace算子在一般几何流演化下的一些梯度估计,推广了Zhu Xiao-bao和Deng Yi-hua的结果...     

EXISTENCE AND UNIQUENESS OF WEAK SOLUTIONS FOR TWO-DIMENSIONAL MODIFIED NAVIER-STOKES EQUATIONS

This paper studies a two-dimensional modified Navier-stokes equations. The author shows the existence and uniqueness of weak solutions for this equation by Galerkin method in bounded domains. The result is further extended to the case of unbounded channel-like domains.     

复微分方程组亚纯解的分量的Nevanlinna特征估计

本文讨论了一类复微分方程组的亚纯解的分量的Nevanlinna特征估计,利用亚纯函数Nevanlinna值分布理论,得到了一个有关方程组亚纯解的分量的Nevanlinna特征估计定理.该结果推广了高凌云等人的一些结果.     

一类二阶方程的解的收敛性

本文研究一类二阶常微分方程解的渐近性态，假设方程具有正阻尼及适当保证所有解有界的条件成立，我们证明了每个解收敛于奇点，该结果能够用于系统的奇点集是不可数的情形。     

A PRIORI ESTIMATE AND EXISTENCE OF POSITIVE SOLUTIONS FOR SYSTEM OF SEMILINEAR ELLIPTIC EQUATIONS

1.APrioriBounds##DTherearealotofresultsfortheprioriboundsandtheexistenceofpositivesolutionsofsemilinearellipticequations(see[2],[3]).Weshallinvestigatetheprioriboundsandtheexistenceofpositivesolutionsforsystemofellipticboundaryvalueproblems:Wealwaysassume…     

关于一类拟线性拟抛物方程解的Blow─up问题

本文利用Ｆｏｕｒｉｅｒ空间的比较原理研究一类拟线性拟抛物方程解的Ｂｌｏｗ－ｕｐ问题，并给出了其解在有限时刻Ｂｌｏｗ－ｕｐ的条件。     

一类修正的Navier—Stokes方程组Neumann边值问题的弱解

讨论一类修正的Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ型方程组Ｎｅｕｍａｎｎ边值问题的可解性及解的性质。