一类非退化半导体方程弱解渐近性的探讨  

Asymptotic Behavior of Weak Solutions to Non-degenerate Equations in Semiconductors Theory

作　　者：周文华[1] 杨小勇[1] 

机构地区：[1]淮海工学院数理科学系,江苏连云港222005

出　　处：《淮海工学院学报（自然科学版）》2007年第2期5-8,共4页Journal of Huaihai Institute of Technology:Natural Sciences Edition

基　　金：淮海工学院自然科学基金资助项目(Z2005034)

摘　　要：探讨了在初值u0,v0∈L2+(Ω)的条件下,一类非退化半导体方程其混和初边值问题弱解的渐近性.在L2+(Ω)空间上构造了一个熵函数,利用带ε的Cauchy不等式和Poincare不等式及弱解的定义,推导出了此函数满足的一个微分方程不等式,通过求解微分方程,证明了弱解的渐近性问题.主要结论是:在满足一定的假设条件下,在L2+(Ω)空间上当t→∞时,非退化半导体方程的解收敛到热平衡方程的解.This paper probes into the asymptotic behavior of the weak solution to non-degenerate equations in semiconductors theory under the conditions of initial value being u0, v0 ∈L^2 ＋（Ω）. The asymptotic behavior of the weak solution is obtained when an enthalpy function is made in L^2 ＋（Ω） and a differential inequality is proved after using Cauchy inequality, Poincare inequality and the definition of weak solution. The conclusion is that the weak solution to the non--degenerate equations converges to the solution of thermal equilibrium state in L^2 ＋（Ω） as t→∞ if some hypothese are imposed.

关 键 词：半导体方程 弱解 渐近性 

分 类 号：O175.29[理学—数学]