On Stability Of Inverse Analytic Function Boundary Value Problem With Respect To Path Of Boundary

The dissertation discusses several classes of inverse boundary value problems andits stability. With the development in science and technology, more and morepractical problems, such as mechanic, physics and the engineering technology, havebeen formulated into inverse analytic function boundary value problems. This paperfocuses on finding solvability conditions, expression, and its stability.Firstly, we discuss the stability of inverse Hilbert boundary value problem withrespect to path of boundary. The unit circle become approximate circle under thesmall perturbation of boundary curve. With which solving process and its solutionsof the inverse Hilbert boundary value problem are got by applying the knowledge ofconformal mapping theorem. When the index of this problem is non-negative, theerror estimate of the solutions are obtained. Therefore we get the conclusion that thesolution of inverse Hilbert boundary value problem about boundary curve are stable.Secondly, we study the stability of inverse Riemann boundary value problemunder the small perturbation of the infinite line.Giving an presentation for inverseRiemann boundary value problem in the infinite line and the solving process and itssolutions. When the infinite line have smooth perturbation, it no longer be an line,finding that it is difficult to induce the solutions. But we can use the theory ofconformal mapping theory to solve the problem. When the index of this problem isnon-negative, we show the solutions are stable, and give the corresponding errorestimates.Thirdly, the dissertation discusses the stability of the periodic Riemann boundaryvalue inverse problem, giving the presentation of the periodic Riemann boundaryvalue inverse problem. We primarily get the stability of the solution about the certainlimited region, then getting the whole periodic stability through expanding thesolution periodically. We obtain that the solution are stable on the whole region.