Publications
Article · Журнал «Математические заметки СВФУ» · March 30, 2024
Parabolic equations with degeneracy and unknown coefficient
Alexander Ivanovich Kozhanov, Guzel Rashitkhuzhakyzy Ashurova
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.
Differential Equations and Boundary ProblemsNumerical methods in inverse problemsNonlinear Partial Differential Equationsparabolic equationsdegenerate equationsnonlinear inverse problems
More by Guzel Ashurova
- INVERSE PROBLEMS FOR A DOUBLY DEGENERATE THIRD-ORDER DIFFERENTIAL EQUATION WITH MULTIPLE CHARACTERISTICSJournal of Mathematics Mechanics and Computer Science · 2026
- THIRD-ORDER DIFFERENTIAL EQUATIONS WITH MULTIPLE CHARACTERISTICS: DEGENERATION AND UNKNOWN EXTERNAL INFLUENCEЧелябинский физико-математический журнал · 2024 · Citations: 2
- Solvability of Coefficient Inverse Problems of Spatial Type for Parabolic Equations with Varying Involution DirectionJournal of Mathematical Sciences · 2024 · Citations: 2
- Inverse problems of parameter recovery in differential equations with multiple characteristicsJournal of Mathematics Mechanics and Computer Science · 2022 · Citations: 2