Abstract
<p style='text-indent:20px;'>We consider the recovering of the shape of a cavity from the Cauchy datum on an accessible boundary in case of semilinear boundary value problems. Existence and a characterization of the domain derivative of solutions of semilinear elliptic equations are proven. Furthermore, the result is applied to solve an inverse obstacle problem with an iterative regularization scheme. By some numerical examples its performance in case of a Kerr type nonlinearity is illustrated.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Control and Optimization,Discrete Mathematics and Combinatorics,Modeling and Simulation,Analysis,Control and Optimization,Discrete Mathematics and Combinatorics,Modelling and Simulation,Analysis
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