EXISTENCE OF WEAK SOLUTIONS TO A DEGENERATE STEAD-STATE SEMICONDUCTOR EQUATIONS

In this paper, we consider a degenerate steady-state drift-diffusion model for semiconductors. The pressure function used in this paper is ()(s) = s~α(α > 1). We present existence results for general nonlinear diffhsivities for the degenerate Dirichlet-Neumann mixed boundary value problem.     

退化C_0-半群族的指数稳定性

首先,应用泛函分析和算子理论在Hilbert空间中得到了关于退化C_0-半群指数稳定的充分必要条件.然后,讨论了退化C_0-半群族的指数稳定性问题,应用退化C_0-半群理论给出了充分必要条件.     

Chaplygin气体Euler方程组的轴对称解

构造了两维Chaplygin气体Euler方程组的三参数、自相似的弱解.在自相似和轴对称的假设下,两维Chaplygin气体Euler方程组可以化为无穷远边值的常微分方程组,由此得到了解的存在性和解的结构.与多方气体不同的是Chaplygin气体的Euler方程组是完全线性退化的.即使在轴向速度大于零的时候解也会出现间断现象.这些解展示了宇宙演化过程中的一些现象,例如黑洞的形成与演化以及宇宙的暴涨和膨胀.     

General decay and blowup of solutions for coupled viscoelastic equation of Kirchhoff type with degenerate damping terms

In this work, we consider a nonlinear system of viscoelastic equations of Kirchhoff type with degenerate damping and source terms in a bounded domain. Under suitable assumptions on the initial data, the relaxation functions g_i(i = 1,2) and degenerate damping terms, we obtain global existence of solutions. Then, we prove the general decay result. Finally, we prove the finite time blow‐up result of solutions with negative initial energy. This work generalizes and improves earlier results in the literature.     

Lower Bounds of Dirichlet Eigenvalues for General Grushin Type Bi-Subelliptic Operators

Let Q be a bounded open domain in R^n with smooth boundaryаΩ.Let X=(X1,X2…,Xm)be a system of general Grushin type vector fields defined onΩand the boundaryаΩis non-characteristic for X.For△x=∑j=1^mXj^2,we denoteλk as the k-th eigenvalue for the bi-subelliptic operator△X2^2 onΩ.In this paper,by using the sharp sub-elliptic estimates and maximally hypoeliptic estimates,we give the optimal lower bound estimates ofλk for the operatork△X^2.     

Some Examples of Nonhypoelliptic Infinitely Degenerate Elliptic Differential Operators

This paper contains examples of nonhypoelliptic infinitely degenerate elliptic differential operators. Global nonsmooth solutions of the corresponding homogeneous equations are constructed.     

双退缩抛物型方程解的一个性质

在Ｑ＝Ｇ×（０，Ｔ）考虑一类双退缩抛物型方程，在满足较一般的结构条件下，证明了如果它的解在抛物边界等于零，那么必是平凡解．     

Studies of Some Curvature Operators in a Neighborhood of an Asymptotically Hyperbolic Einstein Manifold

On an asymptotically hyperbolic Einstein manifold (M,g₀) for which the Yamabe invariant of the conformal structure on the boundary at infinity is nonnegative, we show that the operators of Ricci curvature, and of Einstein curvature, are locally invertible in a neighborhood of the metric g₀. We deduce in the C^∞ case that the image of the Riemann-Christoffel curvature operator is a submanifold in a neighborhood of g₀.     

An Identification Problem for First-Order Degenerate Differential Equations

We study a first-order identification problem in a Banach space. We discuss the nondegenerate and mainly the degenerate case. As a first step, suitable hypotheses on the involved closed linear operators are made in order to obtain unique solvability after reduction to a nondegenerate case; the general case is then handled with the help of new results on convolutions. Some applications to partial differential equations motivate this abstract approach.Communicated by I. GalliganiWork partially supported by MIUR (Ministero dell’ Istruzione, dell’ Università e dalla Ricerca), Project PRIN 2004011204 “Analisi Matematica nei Problemi Inversi,” and by the University of Bologna Funds for Selected Research Topics.     

关于广义Euler多项式和分式的讨论

This note establishes a pair of exponential generating functions for generalized Eulerian polynomials and Eulerian fractions, respectively. A kind of recurrence relation is obtained for the Eulerian fractions. Finally, a short proof of a certain summation formula is given.