Parabolic equations with degeneracy and unknown coefficient
https://doi.org/10.25587/2411-9326-2024-1-56-69
Abstract
The work is devoted to investigating the solvability in Sobolev spaces of nonlinear inverse problems of determination, along with the solution u(x, t) of a parabolic equation, the unknown coefficient dependent on time. The studied problems are unique since the original parabolic equation is degenerate. As the integral overdetermination conditions, we use domain-wide integral overdetermination conditions or integral boundary overdetermination conditions. The existence and uniqueness theorems are proved for regular solutions, i.e. the solutions having all generalized derivatives included in the corresponding equation.
About the Authors
A. I. Kozhanov
Sobolev Institute of Mathematics; Novosibirsk State University
Russian Federation
Russian Federation
Aleksandr I. Kozhanov
4 Koptyug Avenue, 630090 Novosibirsk
1 Pirogov Street, 630090 Novosibirsk
G. R. Ashurova
Al-Farabi Kazakh National University
Kazakhstan
Kazakhstan
Guzel R. Ashurova
71 Al-Farabi Avenue, 050040 Almaty
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Review
For citations:
Kozhanov A.I., Ashurova G.R. Parabolic equations with degeneracy and unknown coefficient. Mathematical notes of NEFU. 2024;31(1):56-69. (In Russ.) https://doi.org/10.25587/2411-9326-2024-1-56-69
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