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An inverse boundary value problem for a nonlinear wave equation
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An inverse problem for fluidsolid interaction
1.  Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany, Germany 
2.  Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716, United States 
We define an objective functional depending on a nonnegative regularization parameter such that, for any positive regularization parameter, there exists a regularized solution minimizing the functional. Moreover, for the regularization parameter tending to zero, these regularized solutions converge to the solution of the inverse problem provided the latter is uniquely determined by the given far field patterns. The whole approach is based on the variational form of the partial differential operators involved. Hence, numerical approximations can be found applying finite element discretization. Note that, though the transmission problem may have nonunique solutions for domains with socalled Jones frequencies, the scattered field and its far field pattern is unique and depend continuously on the shape of the obstacle.
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