PARABOLIC EQUATIONS WITH DEGENERACY AND UNKNOWN COEFFICIENT
Kozhanov A.I. Ashurova G.R.
January-March 2024M. K. Ammosov North-Eastern Federal University
Mathematical Notes of NEFU
2024#31Issue 156 - 69 pp.
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.
degeneration , existence , integral overdetermination , nonlinear inverse coefficient problems , parabolic equations , regular solutions , uniqueness
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Sobolev Institute of Mathematics, 4 Koptyug Avenue, Novosibirsk, 630090, Russian Federation
Novosibirsk State University, 1 Pirogov Street, Novosibirsk, 630090, Russian Federation
Al-Farabi Kazakh National University, 71 Al-Farabi Avenue, Almaty, 050040, Kazakhstan
Sobolev Institute of Mathematics
Novosibirsk State University
Al-Farabi Kazakh National University
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