一类非线性退化半导体方程弱解存在性的研究  

Existence of solutions on a quasilinear degenerate system arising in semiconductors theory

作　　者：周文华[1] 刘继军[2] 

机构地区：[1]淮海工学院数理科学系,江苏连云港222005 [2]东南大学数学系,江苏南京210096

出　　处：《西北大学学报（自然科学版）》2007年第2期191-196,共6页Journal of Northwest University（Natural Science Edition）

基　　金：国家自然科学基金资助项目(10371018);淮海工学院科研课题基金资助项目(Z2005034)

摘　　要：目的研究非线性退化半导体方程在初值u0,v0∈L2+(Ω)的条件下,其混和初边值问题弱解的存在性。方法利用截断的方法先将原问题正则化,对正则化问题的解做估计,并利用紧性引理。结果通过取极限证明了原问题解的存在性。结论在满足一定假设条件下,非线性退化半导体方程存在弱解。Aim To prove the existence of the weak solution under appropriate conditions such as initial values u0,v0∈L2＋（Ω） when a quasilinear degenerate system arising in semiconductors theory is considered. Methods Make a regularization of the problem by a cut-off method and the compact lemma. Results The limit of the solutions of the regularized problem is a solution of the original problem after estimates. Conclusion The existence of solutions on a quasilinear degenerate system is shown under some conditions.

关 键 词：半线性退化系统 半导体方程 存在性 

分 类 号：O175.29[理学—数学]