An inverse problem for a nonlinear biharmonic operator

Abstract

An inverse problem for a nonlinear biharmonic operator is under consideration in the spirit of Isakov (1993) and Johansson-Nurminen-Salo (2023). We prove that a general nonlinear term of the $Q=Q(x,u,\nabla u,\hat{I}”u)$ associated to a nonlinear biharmonic operator can be recovered from the local Cauchy data set. The proof uses first order linearization method, Runge approximation, and uniqueness results for the linearized inverse problem.

28 pages