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- Resumen es exacto "In this thesis we seek to characterize an unknown three-layer material. To do this, it is necessary to recognize the material that makes up each layer and locate the contact points between each pair of consecutive materials. For this purpose, the material is exposed to a stationary, one-dimensional, simple and non-invasive process of heat transfer. It is considered a bar embedded in a fluid (liquid or gas) is considered to be composed of three consecutive segments with two solid-solid type interfaces, where each section corresponds to an isotropic and homogeneous material. On the left edge, a Dirichlet-type condition is imposed, indicating constant temperature, and on the right, a Robin-type condition to model the convection phenomenon. Finding a solution to this type of problem, knowing all the parameters of the model and the boundary conditions, is called a forward problem. In this work, explicit analytical solutions are obtained using Fourier techniques. The solutions are included in this thesis in order to present a self-contained work. To determine the unknown three-layer material, obtain a more precise mathematical characterization of the phenomenon studied and develop criteria that improve measurement techniques; the estimation of model parameters can be performed. These are called inverse problems and are related to the forward problem. Two inverse problems are dealt with in this thesis. The first inverse problem consists of the simultaneous location of the two points of contact between each pair of materials. To do this, two temperature measurements are used, one in the middle of the bar and another at the right end of it. The second inverse problem consists of determining the materials that make up the bar, based on the estimation of the thermal conductivities of each material. These parameters are obtained using three temperature measurements, one at each interface and another at the right edge of the bar. Both problems are solved analytically and a bound is given for the error made in the approximation of each parameter. In addition, an elasticity analysis is performed to find out the local dependence of each parameter estimated with the data used."
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