Geodesic
Linear inverse problems for degenerate evolution equations with the Gerasimov–Caputo derivative in the sectorial case
Matematičeskie zametki SVFU, Tome 27 (2020) no. 2, pp. 54-76 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We investigate the unique solvability of linear inverse problems for the evolution equation in a Banach space with a degenerate operator at the fractional Gerasimov–Caputo derivative and with a time-independent unknown coefficient. It is assumed that a pair of operators in the equation (at the unknown function and at its fractional derivative) generates a family of resolving operators of the corresponding degenerate linear homogeneous equation of the fractional order. The original problem is reduced to a system of two problems: the problem for an algebraic equation on the degeneration subspace of the original equation and the problem for the equation solved with respect to the fractional derivative, on the complement to the degeneration subspace. Two approaches are demonstrated. The first involves the study of the inverse problem for the equation solved with respect to the derivative and the direct problem for the algebraic equation. In the second approach, the inverse problem for the equation on the degeneration subspace is investigated firstly, then the direct problem for the second equation is researched. Abstract results are used to study initial-boundary value problems for a class of time-fractional order partial differential equations with an unknown coefficient depending on the spatial variables.
Mots-clés : inverse coefficient problem
Keywords: fractional Gerasimov–Caputo derivative, degenerate evolution equation, analytic in a sector resolving family of operators. 
@article{SVFU_2020_27_2_a3,
     author = {A. V. Nagumanova and V. E. Fedorov},
     title = {Linear inverse problems for degenerate evolution equations with the {Gerasimov{\textendash}Caputo} derivative in the sectorial case},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {54--76},
     year = {2020},
     volume = {27},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2020_27_2_a3/}
}
TY  - JOUR
AU  - A. V. Nagumanova
AU  - V. E. Fedorov
TI  - Linear inverse problems for degenerate evolution equations with the Gerasimov–Caputo derivative in the sectorial case
JO  - Matematičeskie zametki SVFU
PY  - 2020
SP  - 54
EP  - 76
VL  - 27
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SVFU_2020_27_2_a3/
LA  - ru
ID  - SVFU_2020_27_2_a3
ER  - 
%0 Journal Article
%A A. V. Nagumanova
%A V. E. Fedorov
%T Linear inverse problems for degenerate evolution equations with the Gerasimov–Caputo derivative in the sectorial case
%J Matematičeskie zametki SVFU
%D 2020
%P 54-76
%V 27
%N 2
%U http://geodesic.mathdoc.fr/item/SVFU_2020_27_2_a3/
%G ru
%F SVFU_2020_27_2_a3
A. V. Nagumanova; V. E. Fedorov. Linear inverse problems for degenerate evolution equations with the Gerasimov–Caputo derivative in the sectorial case. Matematičeskie zametki SVFU, Tome 27 (2020) no. 2, pp. 54-76. http://geodesic.mathdoc.fr/item/SVFU_2020_27_2_a3/