一类带位移的广义Riemann边值问题的封闭形式解  

The closed form solution of generalized Riemann boundary value problem with shift

作　　者：陈金玉[1] 

机构地区：[1]重庆大学自动化学院,重庆400044

出　　处：《福州大学学报（自然科学版）》2015年第5期594-598,共5页Journal of Fuzhou University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(61272043);重庆市基础与前沿研究计划资助项目(cste2013jj B40009)

摘　　要：考虑下述带位移的广义Riemann边值问题Φ+[α(t)]=G1(t)Φ-(t)+G2(t)Φ-(t)+f(t),(t∈L),边界L为简单封闭的Lyapunov曲线,并将复平面C分隔为内域D+和外域D-两部分.正位移或反位移α(t)是曲线L至它自身的同胚变换,且系数满足G1(t),G2(t),f(t),α'(t)∈Hμ(t).讨论当G1(t)±G2(t)之一为常数时,求解并给出了上述问题的封闭形式解,从而得到比前人更好的结果.最后,通过一个实例,验证了求解过程及封闭形式解的正确性.In this paper the generalized Riemann boundary value problem with shift Φ＋[α（ t） ] =G1（t）Φ-（t） ＋G2（t）Φ-（t） ＋f（t）, （t∈L）, is investigated in the class of piecewise analytic func-tions.The boundary L is a simple closed Lyapunov curve in complex plane C, let D＋be the interior domain , and D-=C／D＋,α（ t） is a homeomorphism onto itself which preserves or changes the orien-tation of L, the coefficients G1（t）, G2（t）, f（t）,α′（t） belong to Hμ（t）.When one case of G1（t） ±G2 （ t）≡const is satisfied , the paper establishes the closed form of the solution of problem above , which is better than some past works .Finally, an example is given to verify the correctness of the solu-tion process and the closed form solution .

关 键 词：广义Riemann边值问题 Markushevich问题 位移 共轭 求解 

分 类 号：O174[理学—数学]