Inverse coefficient problem for cascade system of fourth and second order partial differential equations

TL;DR

This paper addresses the inverse problem of recovering a dissipative parameter in a coupled cascade system of fourth and second order PDEs, using optimization and numerical methods to establish stability and effectiveness.

Contribution

It introduces a new approach to solve the coefficient inverse problem for a cascade PDE system, including existence, optimality conditions, and numerical validation.

Findings

Existence of minimizer for the inverse problem

Derivation of necessary optimality conditions

Numerical results demonstrate method effectiveness

Abstract

The study of the paper mainly focusses on recovering the dissipative parameter in a cascade system coupling a bilaplacian operator to a heat equation from final time measured data via quasi-solution based optimization. The coefficient inverse problem is expressed as a minimization problem. We proved that minimizer exists and the necessary optimality condition which plays the crucial role to prove the required stability result for the corresponding coefficient is derived. Utilising the conjugate gradient approach, numerical results are examined to show the method's effectiveness.