Research Article
Unique determination of the initial values of the time-fractional diffusion-wave equation by lateral Cauchy data
Abstract
This paper focuses on the determination of initial values in fractional wave equations. As
is known, there are two initial conditions in fractional wave equations, and we aim to reconstruct these two unknown quantities through the minimum possible lateral Cauchy data.
We construct the Liouville theorem on complex plane cutting of the negative axis, which
helps us to prove the uniqueness of the inverse problem under consideration. In the final
section of this paper, we propose an algorithm that utilizes lateral Cauchy data to recover
the two initial values.
References
- s [1] D.A. Benson, S.W. Wheatcraft and M.M. Meerschaert, Application of a fractional advection-dispersion equation, Water ResourRes. 36 (6), 1403-1412, 20
There are 1 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Partial Differential Equations |
| Journal Section | Mathematics |
| Authors | |
| Early Pub Date | April 11, 2025 |
| Publication Date | |
| Submission Date | July 31, 2024 |
| Acceptance Date | February 18, 2025 |
| Published in Issue | Year 2025 Early Access |