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1.
2.
Recent Progress in the $L_p$ Theory for Elliptic and Parabolic Equations with Discontinuous Coefficients 下载免费PDF全文
Hongjie Dong 《分析论及其应用》2020,36(2):161-199
In this paper, we review some results over the last 10-15 years on elliptic and parabolic equations with discontinuous coefficients. We begin with an approach given by N. V. Krylov to parabolic equations in the whole space with $\rm{VMO}_x$ coefficients. We then discuss some subsequent development including elliptic and parabolic equations with coefficients which are allowed to be merely measurable in one or two space directions, weighted $L_p$estimates with Muckenhoupt ($A_p$) weights, non-local elliptic and parabolic equations, as well as fully nonlinear elliptic and parabolic equations. 相似文献
3.
This paper deals with the Cauchy–Dirichlet problem for the fractional Cahn–Hilliard equation. The main results consist of global (in time) existence of weak solutions, characterization of parabolic smoothing effects (implying under proper condition eventual boundedness of trajectories), and convergence of each solution to a (single) equilibrium. In particular, to prove the convergence result, a variant of the so-called ?ojasiewicz–Simon inequality is provided for the fractional Dirichlet Laplacian and (possibly) non-analytic (but ) nonlinearities. 相似文献
4.
In this paper, we consider a viscoelastic wave equation of variable coefficients in the presence of past history with nonlinear damping and delay in the internal feedback and dynamic boundary conditions. Under suitable assumptions, we establish an explicit and general decay rate result without imposing restrictive assumption on the behavior of the relaxation function at infinity by Riemannian geometry method and Lyapunov functional method. 相似文献
5.
Summary This paper is concerned with the problem of developing numerical integration algorithms for differential equations that, when
viewed as equations in some Euclidean space, naturally evolve on some embedded submanifold. It is desired to construct algorithms
whose iterates also evolve on the same manifold. These algorithms can therefore be viewed as integrating ordinary differential
equations on manifolds. The basic method “decouples” the computation of flows on the submanifold from the numerical integration
process. It is shown that two classes of single-step and multistep algorithms can be posed and analyzed theoretically, using
the concept of “freezing” the coefficients of differential operators obtained from the defining vector field. Explicit third-order
algorithms are derived, with additional equations augmenting those of their classical counterparts, obtained from “obstructions”
defined by nonvanishing Lie brackets. 相似文献
6.
针对VO2薄膜在微测辐射热计上的应用,采用射频反应溅射法,在室温下制备氧化钒薄膜;研究了氧分压对薄膜沉积速率、电学性质及成分的影响.通过调节氧分压,先获得成分接近VO2的非晶化薄膜,再在400℃空气中氧化退火,便可制得高电阻温度系数,低电阻率的VO2薄膜,电阻温度系数约为-4%/℃,薄膜方块电阻为R□为100—300kΩ;薄膜在室温下沉积,400℃下退火的制备方法与微机电加工(micro electromechanic
关键词:
二氧化钒
电阻温度系数
氧分压
射频反应溅射法 相似文献
7.
Ari Sihvola 《Optik》2006,117(7):317-320
A geometric visualization is presented for the Brewster angle for a plane wave reflecting from an interface. The surface is assumed to be isotropic but it is allowed to display both dielectric and magnetic susceptibility, and hence the Brewster (polarizing) angle can attain any value between 0 and 90°, and can exist for both parallel and perpendicular polarizations. The geometric construction (a tetrahedron) is spanned by the basic material parameters of the surface. The Brewster angle appears in one of the faces of the tetrahedron. 相似文献
8.
We consider the problem of maximizing a linear fractional function on the Pareto efficient frontier of two other linear fractional functions. We present a finite pivoting-type algorithm that solves the maximization problem while computing simultaneously the efficient frontier. Application to multistage efficiency analysis is discussed. An example demonstrating the computational procedure is included. 相似文献
9.
TANG Chen ZHANG Fang YAN Hai-Qing CHEN Zhan-Qing LUO Tao 《理论物理通讯》2005,44(3):435-439
We develop the three-step explicit and implicit schemes of exponential fitting methods. We use the three- step explicit exponential fitting scheme to predict an approximation, then use the three-step implicit exponential fitting scheme to correct this prediction. This combination is called the three-step predictor-corrector of exponential fitting method. The three-step predictor-corrector of exponential fitting method is applied to numerically compute the coupled nonlinear Schroedinger equation and the nonlinear Schroedinger equation with varying coefficients. The numerical results show that the scheme is highly accurate. 相似文献
10.
SUN Qiyu 《数学年刊B辑(英文版)》2003,24(3):367-386
In this paper, the author at first develops a method to study convergence of the cascade algorithm in a Banach space without stable assumption on the initial (see Theorem 2.1), and then applies the previous result on the convergence to characterizing compactly supported refinable distributions in fractional Sobolev spaces and Holder continuous spaces (see Theorems 3.1, 3.3, and 3.4). Finally the author applies the above characterization to choosing appropriate initial to guarantee the convergence of the cascade algorithm (see Theorem 4.2). 相似文献