Inverse Coefficient Problem for the Coupled System of Fourth and Second Order Partial Differential Equations

The study of the paper mainly focuses on recovering the dissipative parameter in a coupled system formed by coupling a bilaplacian operator to a heat equation from final time measured output data via a quasi-solution approach with optimization. The inverse coefficient problem is expressed as a minimization problem. We establish the existence of a minimizer and extract the necessary optimality condition, which is essential in proving the requisite stability result for the inverse coefficient problem. The effectiveness of the proposed approach is demonstrated through an analysis of numerical results using the conjugate gradient approach.