Identification of Nonlinear Coefficients in Hyperbolic PDEs, with Application to Piezoelectricity

In this paper we consider the problem of determining parameters in nonlinear partial differential equations of hyperbolic type from boundary measurements. In order to investigate the qualitative behavior of this class of identification problems, we analyze the model problem of identifying c in the nonlinear wave equation dtt − (c(d x)d x)x = 0 and discuss stability and identifiability for this problem. Moreover, we derive applicability of these results to material parameter identification in piezoelectricity and provide numerical reconstruction results.

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