INVERSE COEFFICIENT PROBLEM FOR THE FOURTH-ORDER BEAM EQUATION BY THE METHOD OF VARIATIONAL IMBEDDING

This paper presents an inverse problem related to a fourth-order beam equation, where the coefficient at the zeroth-order term is unknown. Based on the simple approximation lemma, we employ a technique known as the method of variational imbedding to establish the existence and uniqueness of a weak solution for a variational problem. Finally, we provide several numerical examples using the finite difference method to demonstrate the efficiency and accuracy of our proposed approach.