指数型二系性的粗糙度

3 粗糙度 本节是讨论指数型二分性的粗糙度问题,即探讨一个具有指数型二分性的线性系统在保持指数型二分性的前提,系数矩阵可扰动的范围。 首先我们用一种简单的方法来证明指数型二分性的粗糙度理论。 指数型二分性粗糙定理:若(4.1)是有界线性系统,且具有指数型二分性,则存在常数δ>0,只要时,线性系统(4.2)也具有指数型二分性。 证明:由定理2.7的必要性,存在有界连续、分段C′的可逆实对称矩阵函数G(t),使得对于任意向量x ∈R^n,在G(t)的C′点满足:

A Property of Solutions for Elliptic Equation with Nonstandard Growth Conditions in Unbounded Domain

In this paper the author proves that the Phragmen Lindelof principle holds for solutions of elliptic equation (1) with nonstandard growth conditions.

Blowup Criteria for Full Compressible Navier-Stokes Equations with Vacuum State

This paper deals with the global strong solution to the three-dimensional(3D)full compressible Navier-Stokes systems with vacuum. The authors provide a sufficient condition which requires that the Sobolev norm of the temperature and some norm of the divergence of the velocity are bounded, for the global regularity of strong solution to the 3D compressible Navier-Stokes equations. This result indicates that the divergence of velocity fields plays a dominant role in the blowup mechanism for the full compressible Navier-Stokes equations in three dimensions.