R^2中变形Helmholtz方程的某些边值问题  

Some boundary value problems for the modified Helmholtz equations in R^2

作　　者：王斌[1] 杨丕文[2] 

机构地区：[1]雅安职业技术学院教育系,四川雅安625000 [2]四川师范大学数学系,四川成都610066

出　　处：《西南民族大学学报（自然科学版）》2016年第3期324-328,共5页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：国家自然科学基金项目(61173121);高校博士点基金(20095134110001);四川省教育厅重点项目(12ZA136)

摘　　要：在空间物理,核物理,激光和电子技术等应用领域,有很多与Helmholtz方程以及变形Helmholtz方程相关的边值问题,但目前针对性的研究成果还很少.研究了变形Helmholtz方程的一类Riemann-Hilbert边值问题,利用复方程相关理论,讨论了在不同条件下其解的存在性和唯一性,并得出了可解性定理,利用获得的结果,讨论了单位圆G上的二阶变形Helmholtz方程的斜微商边值问题.In the application field of space physics,nuclear physics,laser and electronic technology,there are many Helmholtz equations and Modified Helmholtz equation associated with the boundary value problem. However,the targeted researches on the issues are rare at present. By using the methods from complex equation,this paper studies a class of Riemann-Hilbert boudary value problems for Modified Helmholtz equation and discusses its solvability and uniqueness in different cases. The theorems of solvability of the problems are obtained. In addition,this paper studies the oblique derivative boundary value problems for the Modified Helmholtz equation of second order on the unit disk by using the preceding results.

关 键 词：变形Helmholtz方程 RIEMANN-HILBERT边值问题 斜微商边值问题 

分 类 号：O175.8[理学—数学]