Coefficient identification in the Euler-Bernoulli equation using regularization methods

In this paper, we will study the inverse problem of identification of flexural rigidity coefficient in the Euler-Bernoulli equation. This inverse problem is ill-posed. To solve it, we will use regularization methods. In particular, we will apply the mollification method and the Landweber iteration method, in particular, to find the regularized solution of the Moore-Penrose generalized inverse to a linear operator and with this, we reconstruct the coefficient. At the end of this paper, will present some examples of interest.