Approximate Solution for a Biharmonic Problem Outside a Quarter Circle

Abstract

This paper investigates an inverse boundary value problem for the biharmonic equation in the exterior of a quarter circle. The problem is shown to be ill-posed in the sense of Hadamard. Using the Almansi decomposition, it is reduced to two harmonic problems, which are solved by separation of variables and Fourier series expansion. An explicit solution representation is derived, and a truncated Fourier regularization method is proposed for stable reconstruction from noisy boundary data. A logarithmic stability estimate and a convergence result are established.