Inverse linear problems for a certain class of degenerate fractional evolution equations

V. E. Fedorov ; A. V. Nagumanova

Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics". Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part III, Tome 167 (2019), pp. 97-111.

Résumé

In this paper, we study the unique solvability of linear inverse coefficient problems with a time-independent unknown coefficient for evolution equations in Banach spaces with degenerate operators acting on the Gerasimov–Caputo fractional derivative. We apply abstract results obtained in the paper to the study of inverse problems with undetermined coefficients depending only on spatial variables for equations with polynomials on a self-adjoint, elliptic differential operator with respect to spatial variables. Also, we apply general results to the study of the unique solvability of inverse problems for time-fractional Sobolev systems.

Détail

Mots-clés : inverse coefficient problem
Keywords: degenerate evolution equation, Gerasimov–Caputo fractional derivative.

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