Related papers: Some Unexplored Topics in The Reconstruction of Sc…
In the paper, we propose an analytical and numerical approach to identify scalar parameters (coefficients, orders of fractional derivatives) in the multi-term fractional differential operator in time, $\mathbf{D}_t$. To this end, we analyze…
The problem of recovering coefficients in a diffusion equation is one of the basic inverse problems. Perhaps the most important term is the one that couples the length and time scales and is often referred to as {\it the\/} diffusion…
In this paper we study the simultaneous reconstruction of two coefficients in a reaction-subdiffusion equation, namely a nonlinearity and a space dependent factor. The fact that these are coupled in a multiplicative matter makes the…
When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model related to orders of the fractional derivatives, are often unknown and difficult to be…
In this work, we investigate an inverse problem of recovering multiple orders in a time-fractional diffusion model from the data observed at one single point on the boundary. We prove the unique recovery of the orders together with their…
A standard inverse problem is to determine a source which is supported in an unknown domain $D$ from external boundary measurements. Here we consider the case of a time-dependent situation where the source is equal to unity in an unknown…
In this work, we investigate the recovery of a parameter in a diffusion process given by the order of derivation in time for a class of diffusion type equations, including both classical and time-fractional diffusion equations, from the…
In this article, we consider the reconstruction of $\rho(t)$ in the (time-fractional) diffusion equation $(\partial_t^\alpha-\triangle)u(x,t)=\rho(t)g(x)$ ($0<\alpha \le 1$) by the observation at a single point $x_0$. We are mainly…
We consider the problem of reconstructing the position and the time-dependent optical properties of a linear dispersive medium from OCT measurements. The medium is multi-layered described by a piece-wise inhomogeneous refractive index. The…
There has been considerable recent study in "sub-diffusion" models that replace the standard parabolic equation model by a one with a fractional derivative in the time variable. There are many ways to look at this newer approach and one…
This work is concerned with numerically recovering multiple parameters simultaneously in the subdiffusion model from one single lateral measurement on a part of the boundary, while in an incompletely known medium. We prove that the boundary…
Inverse problem to recover simultaneously a scalar coefficient, order of a time-fractional derivative, parameters of multiterm fractional Laplacian and a time-dependent source term occurring in a superdiffusion equation from measurements…
The focus of this paper is on the concurrent reconstruction of both the diffusion and potential coefficients present in an elliptic/parabolic equation, utilizing two internal measurements of the solutions. A decoupled algorithm is…
This article considers the problem of reconstructing unknown driving forces based on incomplete knowledge of the system and its state. This is studied in both a linear and nonlinear setting that is paradigmatic in geophysical fluid dynamics…
This work considers the subdiffusion problem with non-positive memory, which not only arises from physical laws with memory, but could be transformed from sophisticated models such as subdiffusion or subdiffusive Fokker-Planck equation with…
The article investigates an algorithm for identifying an unknown constant parameter for a scalar regression model using a nonlinear operator that allows us to obtain a new regression equation (with an expanded number of unknown parameters)…
This paper considers the inverse problem of recovering state-dependent source terms in a reaction-diffusion system from overposed data consisting of the values of the state variables either at a fixed finite time (census-type data) or a…
The aim of this paper is to discuss potential advances in PET kinetic models and direct reconstruction of kinetic parameters. As a prominent example we focus on a typical task in perfusion imaging and derive a system of…
When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model, for example, the orders of the fractional derivative or the source term, are often unknown,…
We consider the problem of asymptotic reconstruction of the state and parameter values in systems of ordinary differential equations. A solution to this problem is proposed for a class of systems of which the unknowns are allowed to be…