低温等离子模型中的一个混合型方程的闭Dirichlet问题  

On Closed Dirichlet Problem for a Mixed-Type Equation in the Cold Plasma Model

作　　者：屈爱芳[1] 

机构地区：[1]中国科学院武汉物理与数学研究所,武汉430071

出　　处：《数学年刊（A辑）》2011年第2期245-256,共12页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.10531020);973计划(No.2006CB805902)资助的项目

摘　　要：描述理想的低温等离子体中电磁波传播的模型是一个椭圆双曲混合型方程.证明了该方程闭Dirichlet问题弱解的存在唯一性.该结果关于区域的几何结构要求较少.由于这里所讨论的方程的奇异性与Keldysh方程的奇异性有相似性质,而后者的奇异性比Tricomi方程更强,因此关于其正则性的研究是很有意义的.作者给出了一个内正则性结果.A mixed elliptic hyperbolic equation arises in models for electromagnetic wave propagation in cold plasma. The existence and uniqueness of a weak solution to the closed Dirichlet boundary value problem for the equation of mixed type is proven. Few restrictions on the boundary geometry of the domain is required. Since the singularity of the equation discussed here has the same property as that of the Keldysh equation, which is stronger than that of the Tricomi equation, it is meaningful to know about its regularity. An interior regularity result is given here.

关 键 词：低温等离子体模型 双曲椭圆混合型方程 闭边值问题 内正则性 

分 类 号：O175.28[理学—数学]