Linear inverse problems for integro-differential equations in Banach spaces with a bounded operator

V. E. Fedorov ; A. D. Godova

Contemporary Mathematics. Fundamental Directions, Proceedings of the Voronezh Winter Mathematical Krein School — 2024, Tome 70 (2024) no. 4, pp. 679-690

Résumé

In this paper, we study the questions of well-posedness of linear inverse problems for equations in Banach spaces with an integro-differential operator of the Riemann–Liouville type and a bounded operator at the unknown function. A criterion of well-posedness is found for a problem with a constant unknown parameter; in the case of a scalar convolution kernel in an integro-differential operator, this criterion is formulated as conditions for the characteristic function of the inverse problem not to vanish on the spectrum of a bounded operator. Sufficient well-posedness conditions are obtained for a linear inverse problem with a variable unknown parameter. Abstract results are used in studying a model inverse problem for a partial differential equation.

Détail

Keywords: inverse problem, integro-differential equation, Riemann–Liouville type operator, well-posedness.

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