An inverse problem for an expanding heated tube
Donna Sylvester · Inverse Problems · 1997
In this paper, we study a one-dimensional model of an expanding material which is immersed in a heated bath at constant temperature. In the physical domain (i.e. Eulerian coordinates), the equations governing the temperature in the expanding slab involve several flux terms. We introduce Lagrangian coordinates to simplify the equations. We show that, under a variety of hypotheses, the nonlinear coefficient of thermal expansion can be deduced from observing the width as a function of time in a single experiment.