High Order Regularity for Interface Problems

Interface problems for second order elliptic partial differential equations are studied. We prove that each weak solution can be decomposed into two parts near singular points, one of which is a linear combination of some particular solutions,and the other one belongs to H where s≥2 is arbitrary.     

Viscosity splitting method for three dimensional Navier-Stokes equations

Three dimensional initial boundary value problem of the Navier-Stokes equation is considered. The equation is split in an Euler equation and a non-stationary Stokes equation within each time step. Unlike the conventional approach, we apply a non-homogeneous Stokes equation instead of homogeneous one. Under the hypothesis that the original problem possesses a smooth solution, the estimate of theH ^s+1 norm, 0≦s<3/2, of the approximate solutions and the order of theL ² norm of the errors is obtained. This work was supported by the Science Foundation of Academia Sinica under grant (84)-103.     

Existence,uniqueness and convergence as vanishing viscosity for a reaction-diffusion-convection system

A simple qualitative model of dynamic combustion

INTERFACE PROBLEMS FOR ELLIPTIC DIFFERENTIAL EQUATIONS

ＩＮＴＥＲＦＡＣＥＰＲＯＢＬＥＭＳＦＯＲＥＬＬＩＰＴＩＣＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＹＩＮＧＬＵＮＧＡＮＡｂｓｔｒａｃｔＡｎｅｗａｐｐｒｏａｃｈｉｓｇｉｖｅｎｔｏａｎａｌｙｓｅｔｈｅｒｅｇｕｌａｒｉｔｙｏｆｓｏｌｕｔｉｏｎｓｎｅａｒｓ...     

INFINITE ELEMENT METHOD FOR PROBLEMS ON UNBOUNDED AND MULTIPLY CONNECTED DOMAINS

1 IntroductionDifferent kinds of numerical n1etl1ods llavc been apPlied to so1lle proble1l1s o11 exteriordolllai11s successf1lly, e.g. tlle bou11dary element metl1od, the absorbillg boundary condi-tion lnethod, the spectrunl 11letllod, a11d the i11fillite eleIue1lt 1nethod. Tlle il1finite elementllletllod llas beell applied to tl1e Laplace equatioll['], the Stokes equation[']['], the plane elastic-ity systeln['1, alld the Heln1ho1tz equatioll[n. We study tl1e infinite ele111ent llletl1od tbr…     

三维Stokes绕流问题的无限元逼近(英文)

设计了一种最少自由度的无限元方法来实现三维Stokes绕流问题的求解.通过验证强制性和inf-sup条件,我们证明了相应的离散混合变分问题解的适定性,并在加权Sobolev空间中得到了误差的先验估计.数值实验结果验证了解的收敛性.     

Spectroelectrochemical Properties and Catalytic Activity in Cyclohexane Oxidation of the Hybrid Zr/Hf-Phthalocyaninate-Capped Nickel(II) and Iron(II) tris-Pyridineoximates and Their Precursors

The in situ spectroelectrochemical cyclic voltammetric studies of the antimony-monocapped nickel(II) and iron(II) tris-pyridineoximates with a labile triethylantimony cross-linking group and Zr(IV)/Hf(IV) phthalocyaninate complexes were performed in order to understand the nature of the redox events in the molecules of heterodinuclear zirconium(IV) and hafnium(IV) phthalocyaninate-capped derivatives. Electronic structures of their 1e-oxidized and 1e-electron-reduced forms were experimentally studied by electron paramagnetic resonance (EPR) spectroscopy and UV−vis−near-IR spectroelectrochemical experiments and supported by density functional theory (DFT) calculations. The investigated hybrid molecular systems that combine a transition metal (pseudo)clathrochelate and a Zr/Hf-phthalocyaninate moiety exhibit quite rich redox activity both in the cathodic and in the anodic region. These binuclear compounds and their precursors were tested as potential catalysts in oxidation reactions of cyclohexane and the results are discussed.     

Long-time Asymptotic Behavior of Lax-Friedrichs Scheme

In this paper we investigate the asymptotic stability of the discrete shocks of the Lax-Friedrichs scheme for hyperholic systems of conservation laws. For single equations, we show that the discrete shocks of the Lax-Friedrichs scheme are asymptotically stable in the sense of I³ and I¹. For the systems of conservation laws, if the summation of initial perturbations equals to zero, we show the l² stability and l¹ boundedness.