Inverse Boundary Value Problem for Anisotropic Heat Operators

As a mathematical model of thermography, a reconstruction scheme called the dynamical probe method is given for identifying unknown separated inclusions inside a known anisotropic heat conductor. The heat conductivities of inclusions can be also anisotropic. The measured data is the so called Neumann to Dirichlet map which is a mathematical idealization of many measurements consisting of injecting heat flux and measuring the corresponding heat distribution on the part of the boundary of the known heat conductor by infrared camera for any fixed time interval. This idealization becomes relevant if we have for instance the cooling boundary condition on the other part of the boundary. This is due to the exponential decay of temperature in time which enables to conduct many measurements in a short time.