| Issue |
ESAIM: COCV
Volume 31, 2025
|
|
|---|---|---|
| Article Number | 65 | |
| Number of page(s) | 20 | |
| DOI | https://doi.org/10.1051/cocv/2025043 | |
| Published online | 30 July 2025 | |
Stability in Inverse Problem for a Moore–Gibson–Thompson Equation with Time-Dependent Coefficient
1
School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710129, PR China
2
School of Mathematics, Jilin University, Changchun 130012, PR China
* Corresponding author: yuyy122@jlu.edu.cn
Received:
22
April
2024
Accepted:
4
May
2025
In this paper, we consider the inverse problem of determining a time-dependent variable “damping” coefficient depending on a viscosity of the fluid appearing in the Moore–Gibson–Thompson equation. This equation arises, e.g., as a linearization of a model that describes the ultrasound wave propagation in viscous thermally relaxing fluids, and displays a variety of dynamical behaviors. For the inverse problem considered in this work, with all the initial data involved, we obtain a stability result of recovering the time-dependent viscosity by means of geometric optics solutions, and the property of some integral transforms.
Mathematics Subject Classification: 35R30
Key words: Moore–Gibson–Thompson equation / inverse problems / integral transforms / uniqueness / stability
© The authors. Published by EDP Sciences, SMAI 2025
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