Determining the source term in an abstract parabolic problem from a time integral of the solution
DOI:
https://doi.org/10.6092/issn.2240-2829/2670Abstract
Consideriamo il problema della ricostruzione del termine di sorgente in un'equazione astratta di tipo parabolico. L'informazione supplementare, necessaria per la determinazione della soluzione del sistema e della parte incognita del termine di sorgente, è data dalla conoscenza di un integrale della soluzione rispetto alla variabile temporale e a una certa misura di Borel. Presento un teorema di esistenza e unicità di una soluzione, che è anche di regolarità massimale. Esamino alcuni casi particolari, assieme al fatto che talvolta il problema gode di una sorta di proprietà dell'alternativa di Fredholm.
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