兩類調(diào)和方程的狄利克雷問題的解法和調(diào)和函數(shù)極值原理的研究.pdf

1、華中師范大學(xué)碩士學(xué)位論文兩類調(diào)和方程的狄利克雷問題的解法和調(diào)和函數(shù)極值原理的研究姓名：傅秋桃申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：張正杰20070526⑥碩士學(xué)位論文MAS’FER4S1HESlSAbstractInthispaper，wefirstlygavetheexpressionoflaplaceoperatorunderthecylindricalcoordinatesusingvariationalprincipleTh

2、enweinferedtwosolvingmethodsoftwoharmonicfunctions’DirichletproblemThereafterweprovedtheextremumprinciplebyhopflemmaThepapermainlyconsistsofthefollowingparts：ChapteroneintroducedsomeknowledgeofharmonicfunctionsChaptertwo

3、gavetheexpressionoflaplaceoperatorunderthecylindricalc。ordinatesusingvariationalprincipleTheexpressionis△“=ii。O(r8。U)聲孚搴Chapterthreeinferedtwosolvingmethodsofthefollowingtwoproblem(problemoneandproblemtwo)andcomparedthem

4、Problemone：DirichletproblemofcirclelAu=o，pa訓(xùn)：一cos妒(Aisacom刪)Problemtwo：boundaryvalueproblem““Z一竺。『=o’x‘yz‘1(p，只伊)expresse。b。11c。。rdinate)l“p，0，妒)l=3cos201”””。。Chapterfourprovedtheimportantpropertyofharmonicfunctionswhich