Moving Heat Source Reconstruction from the Cauchy Boundary Data

Graduate School of Mathematical Sciences Komaba, Tokyo, Japan Reconstruction of a Moving Boundary from Cauchy Data in One Dimensional Heat Equation

In this paper, we propose a new numerical method for determining a moving boundary from Cauchy data in one dimensional heat equation. The numerical scheme is based on the use of fundamental solutions of the heat equation as basis functions. In order to regularize the ill-conditioned linear system of equations resulted by collocating boundary data, we apply successfully the Tikhonov regularizati...

Reconstruction of an Unknown Boundary Portion from Cauchy Data in <em>N</em>- Dimensions

We consider the inverse problem of determining the shape of some inaccessible portion of the boundary of a region in n dimensions from Cauchy data for the heat equation on an accessible portion of the boundary. The inverse problem is quite ill-posed, and nonlinear. We develop a Newton-like algorithm for solving the problem, with a simple and efficient means for computing the required derivative...

Reconstruction of an Unknown Boundary Portion from Cauchy Data in N-dimensions

We consider the inverse problem of determining the shape of some inaccessible portion of the boundary of a region in n dimensions from Cauchy data for the heat equation on an accessible portion of the boundary. The inverse problem is quite ill-posed, and nonlinear. We develop a Newton-like algorithm for solving the problem, with a simple and efficient means for computing the required derivative...

Image Reconstruction from Incomplete Data

Image Reconstruction from Incomplete Data