Related papers: Regularization operators for identifying the unkno…
Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some…
We address the initial source identification problem for the heat equation, a notably ill-posed inverse problem characterized by exponential instability. Departing from classical Tikhonov regularization, we propose a novel approach based on…
Neural networks have emerged as effective tools for solving ill-posed inverse problems. In many scientific applications, however, observational training data are insufficient, and learned inverse operators must instead be trained on…
In this paper, we investigate the direct and linear inverse problems of identifying time-dependent and time-independent source terms in a time-fractional diffusion-wave equation, using measured data at an interior point of the time…
We introduce a minimization formulation for the determination of a finite-dimensional, time-dependent, orthonormal basis that captures directions of the phase space associated with transient instabilities. While these instabilities have…
We consider the first and half order time fractional equation with the zero initial condition. We investigate an inverse source problem of determining the time-independent source factor by the data at an arbitrarily fixed time and we…
We determine the space-dependent source term for a two-parameter fractional diffusion problem subject to nonlocal non-self-adjoint boundary conditions and two local time-distinct datum. A bi-orthogonal pair of bases is used to construct a…
In this paper, we consider an inverse space-dependent source problem for a time-fractional diffusion equation. To deal with the ill-posedness of the problem, we transform the problem into an optimal control problem with total variational…
This paper is concerned with the inverse moving source problems for parabolic equations. Given the temporal function, we prove the uniqueness of the nonlinear inverse problem of determining the orbit function by final data measured in a…
This paper investigates an inverse source problem for space-time fractional diffusion equations from a posteriori interior measurements. The uniqueness result is established by the memory effect of fractional derivatives and the unique…
This article addresses the inverse source problem for a nonlocal heat equation involving the fractional Laplacian. The primary goal is to reconstruct the spatial component of the source term from partial observations of the system's state…
Fractional calculus provides a rigorous mathematical framework to describe anomalous stochastic processes by generalizing the notion of classical differential equations to their fractional-order counterparts. By introducing the fractional…
In this paper, we consider an inverse problem to determine a source term in a parabolic equation, where the data are obtained at a certain time. In general, this problem is ill-posed, therefore the Tikhonov regularization method is proposed…
This article is concerned with the inverse problem on determining the temporal component of the source term in a coupled system of time-fractional diffusion equations by single point observation. Under a non-degeneracy condition on the…
Here we discuss a regularized version of the factorization method for positive operators acting on a Hilbert Space. The factorization method is a qualitative reconstruction method that has been used to solve many inverse shape problems. In…
Selecting the best regularization parameter in inverse problems is a classical and yet challenging problem. Recently, data-driven approaches have become popular to tackle this challenge. These approaches are appealing since they do require…
In this paper, we study an inverse problem for identifying the initial value in a space-time fractional diffusion equation from the final time data. We show the identifiability of this inverse problem by proving the existence of its unique…
This paper is dedicated to addressing the simultaneous inversion problem involving the initial value and space-dependent source term in a time-fractional diffusion-wave equation. Firstly, we establish the uniqueness of the inverse problem…
Stabilization of a class of time-varying parabolic equations with uncertain input data using Receding Horizon Control (RHC) is investigated. The diffusion coefficient and the initial function are prescribed as random fields. We consider…
This paper considers the temporal discretization of an inverse problem subject to a time fractional diffusion equation. Firstly, the convergence of the L1 scheme is established with an arbitrary sectorial operator of spectral angle $< \pi/2…