The Solutions Of Inverse Compound Boundary Value Problems For Certain Analytic Functions

The boundary value problems for analytic functions is a very important branch ofcomplex function theory,which is widely used in physics, mechanics and engineeringpractical problems,and there are abundant and mature research results.However, inthe wave of today’s science and technology revolution,the researches of positiveproblem can not meet the development in mechanics, physics and engineeringtechnology, so more and more inverse problems always need to be solved.Therefore,studying the inverse boundary value problem for analytic functions not only enrichesthe theory of boundary value problems for analytic functions, but also it is supposedto provide a theoretical basis for solving the inverse problem of other disciplines.This paper mainly consists of the following three questions:Question one:The inverse compound boundary value problems for analyticfunctions.The formulation of inverse compound boundary value problems foranalytic functions in the regions by a group of smooth closed curves is given, andthe method of solving is also given, namely using the elimination method to convertit into the compound boundary value problems,by this way it is obtained that anunknown analytic functions of the solutions of inverse compound boundary valueproblems.The obtained analytic function is substituted into the boundary valueconditions of inverse compound boundary value problems, then using the Plemeljformulas on the closed curve and other calculation methods and techniques ofcomplex function theory, finally,getting the unknown boundary functions ofsolutions of the inverse boundary value problems. Thus, all of the integralrepresentations and the solvable conditions of the solutions of inverse boundaryvalue problems are both obtained.Question two: The inverse compound boundary value problems for analyticfunctions in half-plane.The formulation of inverse compound boundary valueproblems for analytic functions in half-plane is given, and the method of solving isalso given, namely utilizing the elimination method,which can be converted into thecompound boundary value problems in the half-plane to solve, and obtaining anunknown analytic functions of the solutions of inverse compound boundary valueproblems in half-plane.The obtained analytic functions is substituted into theboundary value conditions of inverse compound boundary value problems,thenusing the Plemelj formulas on real axis and other calculation methods and techniquesof the complex function theory, etc,finally, the unknown boundary function ofsolutions of the inverse boundary value problems is received. Therefore, all of theintegral representations and the solvable conditions of the solutions of inverseboundary value problem are both obtained.Question three:Extending the question two to the inverse compound boundary value problem for analytic functions on a class of infinite straight line. Firstly, thecompound boundary value problems for analytic functions on a class of infinitestraight line is discussed,then obtaining the integral representations and the solvableconditions of the solutions of the compound boundary value problems.Afterthat,extending the second question,so the formulation of inverse compoundboundary value problems for analytic functions on a class of infinite straight line isgiven,and they are also obtained all of the integral representations of and thesolvable conditions the solutions of inverse boundary value problems.