# Identification of time-varying source term in time-fractional diffusion equations

@article{Kian2022IdentificationOT, title={Identification of time-varying source term in time-fractional diffusion equations}, author={Yavar Kian and Eric Soccorsi and Qi Xue and Masahiro Yamamoto}, journal={Communications in Mathematical Sciences}, year={2022} }

This paper is concerned with the inverse problem of determining the time and space dependent source term of diffusion equations with constant-order time-fractional derivative in (0, 2). We examine two different cases. In the first one, the source is the product of two spatial and temporal terms, and we prove that both of them can be retrieved by knowledge of one arbitrary internal measurement of the solution for all times. In the second case, we assume that the first term of the product varies…

## 7 Citations

### Uniqueness of inverse source problems for time-fractional diffusion equations with singular functions in time

- Mathematics
- 2022

We consider a fractional diffusion equations of order α ∈ (0, 1) whose source term is singular in time: (∂ t + A)u(x, t) = μ(t)f(x), (x, t) ∈ Ω × (0, T ), where μ belongs to a Sobolev space of…

### Logarithmic stable recovery of the source and the initial state of time fractional diffusion equations

- Mathematics
- 2021

. In this paper we study the inverse problem of identifying a source or an initial state in a time-fractional diﬀusion equation from the knowledge of a single boundary measurement. We derive…

### Equivalence of definitions of solutions for some class of fractional diffusion equations

- Mathematics
- 2021

We study the unique existence of weak solutions for initial boundary value problems associated with different class of fractional diffusion equations including variable order, distributed order and…

### Recovering multiple fractional orders in time-fractional diffusion in an unknown medium

- MathematicsProceedings of the Royal Society A
- 2021

This work proves the unique recovery of the orders together with their weights, which does not require a full knowledge of the domain or medium properties, e.g., the diffusion and potential coefficients, initial condition and source in the model.

### Reconstruction of a Space-Time Dependent Source in Subdiffusion Models via a Perturbation Approach

- MathematicsSIAM J. Math. Anal.
- 2021

The inverse problems of recovering a space-time dependent source component from the lateral boundary observation in a subidffusion model is studied and a well-posedness and a conditional stability result are established.

### Simultaneous determination of coefficients and internal source of a diffusion equation from a single measurement

- Mathematics
- 2020

This article is devoted to the inverse problem of determining simultaneously several class of coefficients and an internal source (a source term or an initial condition) appearing in a diffusion…

### Simultaneous determination of coefficients, internal sources and an obstacle of a diffusion equation from a single measurement

- Mathematics
- 2020

This article is devoted to the simultaneous resolution of three inverse problems, among the most important formulation of inverse problems for partial differential equations, stated for some class of…

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