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...

The propagation of thermal shock waves under the Maxwell–Cattaneo hyperbolic heat conduction theory is considered. In particular, the thermal conductivity is allowed to dependent on the temperature, which makes the model nonlinear. A solution for the evolution of a discontinuity under the linearized version of the governing equations is found via singular surface theory. Then, the Rankine–Hugon...

This paper describes reconstruction of the heat transfer coefficient occurring in the boundary condition of the third kind for the time fractional heat conduction equation. Fractional derivative with respect to time, occurring in considered equation, is defined as the Caputo derivative. Additional information for the considered inverse problem is given by the temperature measurements at selecte...

We consider two dimensional inverse steady state heat conduction problems in complex geometries. The coefficients of the elliptic equation are assumed to be non-constant. Cauchy data are given on one part of the boundary and we want to find the solution in the whole domain. The problem is ill–posed in the sense that the solution does not depend continuously on the data. Using an orthogonal coor...