DETERMINATION OF A SPACEWISE DEPENDENT HEAT SOURCE IN BIHARMONIC HEAT EQUATION FROM FINAL TEMPERATURE MEASUREMENTS

. The paper deals with the inverse problem associated with the biharmonic heat equation, aiming to recover a space -dependent heat source and the temperature distribution based on measurements of the final temperature. The study establishes both the existence and uniqueness of the classical solution, as well as the existence and uniqueness of the generalized solution. These results are attained through the application of the method of series expansion in terms of eigenfunctions for the Dirichlet bi-Laplacian.