Related papers: A source identification problem in a bi-parabolic …

We consider the inverse source problem in the parabolic equation, where the unknown source possesses the semi-discrete formulation. Theoretically, we prove that the flux data from any nonempty open subset of the boundary can uniquely…

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…

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 propose in this paper a new numerical method to solve an inverse source problem for general hyperbolic equations. This is the problem of reconstructing sources from the lateral Cauchy data of the wave field on the boundary of a domain.…

In this work, we investigate the stability issue of the inverse problem of determining the locations and time-dependent amplitudes of point sources in a parabolic equation with a non-self adjoint elliptic operator from boundary…

In this paper, we investigate the inverse problem of determining the right-hand side of a subdiffusion equation with a Caputo time derivative, where the right-hand side depends on both time and certain spatial variables. Similar inverse…

This paper investigates an inverse source problem for general semilinear stochastic hyperbolic equations. Motivated by the challenges arising from both randomness and nonlinearity, we develop a globally convergent iterative regularization…

The aim of this paper is to study time-fractional pseudo-parabolic type equations generated by the Dunkl operator. The forward problem is considered and its well-posedness is established. In particular, a prior estimates are obtained in the…

We discuss inverse problems of determining the time-dependent source coefficient for a general class of subelliptic heat equations. We show that a single data at an observation point guarantees the existence of a (smooth) solution pair for…

In this article, we study an inverse problem consisting in the identification of a space-time dependent source term in the Ginzburg-Landau equation from final-time observations. We adopt a weak-solution framework and analyze Tikhonov's…

In this paper, we investigate the inverse problem of determining an unknown time-dependent source term in a semilinear pseudo-parabolic equation with variable coefficients and a Dirichlet boundary condition. The unknown source term is…

This paper delves into the Inverse Stefan problem, specifically focusing on determining the time-dependent source coefficient in the parabolic heat equation governing heat transfer in a semi-infinite rod. The problem entails the intricate…

In this article, we study wavelet collocation methods based on Taylor and Chebyshev wavelets for the source identification in parabolic inverse problem. In the proposed method, highest order derivative is written in terms of Taylor and…

In this paper, we consider the inverse problem of determining the time-dependent source term in the general setting of Hilbert spaces and for general additional data. We prove the well-posedness of this inverse problem by reducing the…

In this article, we investigate inverse source problems for a wide range of PDEs of parabolic and hyperbolic types as well as time-fractional evolution equations by partial interior observation. Restricting the source terms to the form of…

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…

We consider point sources in hyperbolic equations discretized by finite differences. If the source is stationary, appropriate source discretization has been shown to preserve the accuracy of the finite difference method. Moving point…

This paper is devoted to the study of source reconstruction algorithms for coupled systems of heat equations, with either constant or spatially dependent coupling terms, where internal measurements are available from a reduced number of…

A new numerical method to solve an inverse source problem for the radiative transfer equation involving the absorption and scattering terms, with incomplete data, is proposed. No restrictive assumption on those absorption and scattering…

The paper is concerned with parabolic time-periodic boundary value problems which are of theoretical interest and arise in different practical applications. The multiharmonic finite element method is well adapted to this class of parabolic…