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**An adjoint method for proving identifiability of coefficients in parabolic equations.**
*(English)*
Zbl 1273.35314

Summary: This article presents a uniform approach for dealing with the question of uniqueness in the identification of unknown coefficients in parabolic partial differential equations in \(n\) dimensions. It is shown that the unknown coefficients in a parabolic inverse problem are uniquely determined by the given observation(s) if an associated adjoint problem is approximately controllable. Additionally, the method provides an explicit expression for the gradient of an associated output least squares error functional and may provide a means for solving the inverse problem directly. The flexibility of the method is illustrated in examples of identifications involving one or more coefficients in appearing in a single equation or system and based on various boundary and interior observations.

### MSC:

35R30 | Inverse problems for PDEs |