Some classes of degenerate quasilinear equations with Riemann–Liouville derivatives and a sectorial pair of operators
https://doi.org/10.25587/2411-9326-2026-2-5-20
Abstract
We consider the existence and uniqueness of the classical solution to the Showalter–Sidorov-type problem for some classes of quasilinear equations in Banach spaces with fractional Riemann derivatives. Equations with a degenerate operator at the highest order Riemann–Liouville derivative are studied in the case of sectoriality of the pair of operators in the linear part of the equation, i.e., when this pair generates a degenerate resolving family of operators analytic in a sector, and under the assumption that the nonlinear operator does not depend on elements of the degeneration subspace. We proved theorems on local and global unique solvability of the Showalter–Sidorovtype problem for the equation under study. The obtained abstract results are applied to the study of initial boundary value problems for a class of systems of partial differential equations of fractional order in time.
About the Authors
A. S. Avilovich
Chelyabinsk State University
Russian Federation
Russian Federation
Anna S. Avilovich, Mathematical Analysis Department
129 Kashirin Brothers Street, Chelyabinsk 454001
V. E. Fedorov
Chelyabinsk State University
Russian Federation
Russian Federation
Vladimir E. Fedorov, Mathematical Analysis Department
129 Kashirin Brothers Street, Chelyabinsk 454001
A. O. Sagimbaeva
Chelyabinsk State University
Russian Federation
Russian Federation
Angelina O. Sagimbaeva, Mathematical Analysis Department
129 Kashirin Brothers Street, Chelyabinsk 454001
D. N. Karpenko
Chelyabinsk State University
Russian Federation
Russian Federation
Dmitriy N. Karpenko, Mathematical Analysis Department
129 Kashirin Brothers Street, Chelyabinsk 454001
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Review
For citations:
Avilovich A.S., Fedorov V.E., Sagimbaeva A.O., Karpenko D.N. Some classes of degenerate quasilinear equations with Riemann–Liouville derivatives and a sectorial pair of operators. Mathematical notes of NEFU. 2026;33(2):5-20. (In Russ.) https://doi.org/10.25587/2411-9326-2026-2-5-20
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