Stability properties of a crack inverse problem in half space Public
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We study in this thesis an inverse problem that originates in geophysics. In this inverse problem, a fault and a slip field have to be determined from an overdetermined Partial Differential Equation (PDE) in half space. We achieve three main goals: first, an existence and uniqueness theorem for this PDE in adequate functional spaces. Second, we show that our overdetermined PDE (which reflects that in practice, geophysicists use a PDE model and have access to boundary measurements) does make it possible to recover the fault and the slip. Third, we show that this recovery is stable, under the assumption that the fault must be planar.
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