A uniqueness result for the recovery of a coefficient of the heat conduction equation

Abstract

There are industrial applications where the recovery of the coefficients of the heat conduction equation from measurements of the temperature over an open set Ω* is crucial. We analyse the inverse problem of identifying the conductivity coefficient of the heat equation when a zero initial condition is set and single measurements are made. We prove a uniqueness result for a linearized version of this problem in for n odd that does not depend on a hypothesis about the relative position of the support of the unknown function with respect to Ω*. It is an extension, for n odd, of a theorem proved by Elayyan and Isakov. © 2007 IOP Publishing Ltd.