An Operator Method for Investigation of the Stability of Time-Dependent Source Identification Telegraph Type Differential Problems
Abstract
:1. Introduction
2. The Auxiliary Statements
- The element belongs to for all , and the function is continuous on , .
- is twice continuously differentiable on .
- satisfies the DE and initial and additional conditions.
3. The Well-Posedness of SIP (5)
4. Applications
5. Conclusions and Our Future Plans
- In this article, we prove the main theorem of the stability of time-dependant SIPs for the second-order linear ordinary DE in a Hilbert space with SAPDO. In practice, the stability estimates for the solution of three types of time-dependent SIPs for the TDEs are given.
- We are interested in study of the stability of a high order of accuracy difference schemes uniformly with respect to the timestep size of approximate solutions of time-dependant SIPs for TDEs, in which stability is established without any assumptions in respect of the grid steps and Note that absolute stable difference schemes of a high order of accuracy for the initial value problem for the hyperbolic partial differential equations were presented and investigated in paper [46]. Applying the methods of this paper and paper [46], the absolutely stable difference schemes for the numerical solutions of the time-dependent SIPs for TDEs could be investigated. Naturally, the stability of these difference schemes can be proved.
- Investigating the uniform two-step difference schemes and asymptotic formulas for the solution of the time-dependent SIPs for the TDEs
- Study the time-dependent SIP for the stochastic TDE
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
SIP | Source identification problem |
DE | Differential equation |
TDE | Telegraph differential equation |
SAPDO | Self-adjoint positive definite operator |
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Ashyralyev, A.; Al-Hazaimeh, H. An Operator Method for Investigation of the Stability of Time-Dependent Source Identification Telegraph Type Differential Problems. Symmetry 2023, 15, 1957. https://doi.org/10.3390/sym15101957
Ashyralyev A, Al-Hazaimeh H. An Operator Method for Investigation of the Stability of Time-Dependent Source Identification Telegraph Type Differential Problems. Symmetry. 2023; 15(10):1957. https://doi.org/10.3390/sym15101957
Chicago/Turabian StyleAshyralyev, Allaberen, and Haitham Al-Hazaimeh. 2023. "An Operator Method for Investigation of the Stability of Time-Dependent Source Identification Telegraph Type Differential Problems" Symmetry 15, no. 10: 1957. https://doi.org/10.3390/sym15101957