This book summarizes the main analytical and numerical results of
Carleman estimates. In the analytical part, Carleman estimates for
three main types of Partial Differential Equations (PDEs) are
derived. In the numerical part, first numerical methods are
proposed to solve ill-posed Cauchy problems for both linear and
quasilinear PDEs. Next, various versions of the convexification
method are developed for a number of Coefficient Inverse Problems.
General
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