The Robin Coefficient Inversion For Lapalce Equation On A Rectangular Domain

In many science and engineering applications, people often encounter the inversion problems for Robin coefficients, which are quite popular appearing in the detection of metal corrosion, due to the engineering restriction that some boundary data cannot be directly measured. In these cases we need to apply the measurable boundary data to detect the unknown boundary status indirectly. Under the background of this application problem, in this paper, we discuss the inverse problem for the Laplace equation of Robin coefficient on the rectangular area. The model is as follows: we try to identify the Robin coefficient γ(χ) from the measurable Cauchy data{(u(χ,0), uy(χ,0)):x∈(0,π)}.This paper is organized as follows. In the second chapter we introduce some funda-mental concepts related to the Fourier series and Tikhonov regularization, which will be applied in our work. The third chapter we prove the uniqueness of the inverse problem under certain conditions and the conditional stability. The regularizing reconstruction scheme based on the representation of the solution in terms of the series is also proposed, with the convergence analysis. Finally we give some numerical examples to verify our reconstruction schemes.