scholarly journals The Stabilization of the Solution of an inverse Problem for the Pseudoparabolic Equation

2021 ◽  
Vol 2092 (1) ◽  
pp. 012009
Author(s):  
A. Sh. Lyubanova ◽  
A. V. Velisevich
Keyword(s):  
Inverse Problem ◽  
Asymptotic Behavior ◽  
Differential Operator ◽  
Strong Solution ◽  
Second Order ◽  
Unknown Coefficient ◽  
Pseudoparabolic Equation

Abstract The asymptotic behavior of the strong solution to the inverse problem on recovering an unknown coefficient k(t) in a pseudoparabolic equation (u + ηMu) t + Mu + k(t)u = f is investigated. The differential operator M of the second order with respect spacial variables is supposed to be elliptic and selfajoint. It is proved that the solution of the inverse problem stabilizes to the solution of the appropriate stationary inverse problem as t → + ∞.

scholarly journals The Regularity of the Solutions of Inverse Problems for the Pseudoparabolic Equation

2001 ◽  
Vol 14 (4) ◽  
pp. 414-424
Author(s):  
Anna Sh. Lyubanova ◽  
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Continuous Dependence ◽  
Input Data ◽  
Order Term ◽  
Unknown Coefficient ◽  
Pseudoparabolic Equation ◽  
Third Order ◽  
Additional Information ◽  
The Third

The paper discusses the regularity of the solutions to the inverse problems on finding unknown coefficients dependent on t in the pseudoparabolic equation of the third order with an additional information on the boundary. By the regularity is meant the continuous dependence of the solution on the input data of the inverse problem. The regularity of the solution is proved for two inverse problems of recovering the unknown coefficient in the second order term and the leader term of the linear pseudoparabolic equation

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