Inverse problems in partial differential equations

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When scientists and engineers seek to determine properties of the interior of an object (e.g. the human body, the nucleus of an atom, an airplane wing, the earth, or the sun) without penetrating or even accessing the object, the analyze its effect on acoustic, elastic, electromagnetic or quantum mechanical waves. Mathematically, wave propagation is modeled by Partial Differential Equations and the class of problems considered in the proposed research consists in determining the coefficients of such and equation (which encode the unknown medium properties) from available measurements of the solutions (the waves).