Inverse problems can be formulated in terms of determination of an unknown parameter of a system from partial information of the response of this system that we call observations or measurements. These problems take different forms and they are connected with several applications (medical imaging, seismology, finance...). Broadly speaking, one can check that in our daily life we are often confronted to inverse problems through questions like "where this sounds or light comes from?". Beside the multiple applications of inverse problems, from their high non-linearity and ill-posedness, these problems have mathematical interests in their own. In this context, I have focused my attention on problems of determination of coefficients, source terms or non-linear terms appearing in several class of partial differential equations (respectively operators) from observations of the solutions (respectively from information about spectral data). For instance, we can mention the famous question of Calder\'on related to imaging methods like the Electrical Impedance Tomography (EIT), which can be rewritten as: Can one determine the conductivity of a medium by making measurement at the boundary of the domain?
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