Related papers: The Inverse Problem of Reconstructing Reaction-Dif…
We analyze in this paper the performance of a newly developed globally convergent numerical method for a coefficient inverse problem for the case of multi-frequency experimental backscatter data associated to a single incident wave. These…
An encounter-based approach consists in using the boundary local time as a proxy for the number of encounters between a diffusing particle and a target to implement various surface reaction mechanisms on that target. In this paper, we…
We investigate the inverse source problem for the wave equation, arising in photo- and thermoacoustic tomography. There exist quite a few theoretically exact inversion formulas explicitly expressing solution of this problem in terms of the…
The problem of real-time remote tracking and reconstruction of a two-state Markov process is considered here. A transmitter sends samples from an observed information source to a remote monitor over an unreliable wireless channel. The…
The paper deals with reaction-diffusion equations involving a hysteretic discontinuity in the source term, which is defined at each spatial point. Such problems describe biological processes and chemical reactions in which diffusive and…
An inverse scattering problem is formulated for reconstructing optical properties of biological tissues. A recursive linearization algorithm is used to solve the inverse scattering problem. We employed the idea of finite element boundary…
Our aim is to study the backward problem, i.e. recover the initial data from the terminal observation, of the subdiffusion with time dependent coefficients. First of all, by using the smoothing property of solution operators and a…
This paper addresses a factorization method for imaging the support of a wave-number-dependent source function from multi-frequency data measured at a finite pair of symmetric receivers in opposite directions. The source function is given…
Accurate modeling of ultrasound wave propagation is essential for high-fidelity simulation and imaging in ultrasonic testing. A primary challenge lies in characterizing the excitation source, particularly for transducers with large…
This paper investigates the simultaneous identification of a spatially dependent potential and the initial condition in a subdiffusion model based on two terminal observations. The existence, uniqueness, and conditional stability of the…
Two main aims of this paper are to develop a numerical method to solve an inverse source problem for parabolic equations and apply it to solve a nonlinear coefficient inverse problem. The inverse source problem in this paper is the problem…
We study long-time properties of reversible reaction-diffusion systems of type A + B <-> C by means of perturbation expansion in powers of 1/t (inverse of time). For the case of equal diffusion coefficients we present exact formulas for the…
This paper is concerned with backward problem for nonlinear space fractional diffusion with additive noise on the right-hand side and the final value. To regularize the instable solution, we develop some new regularized method for solving…
The present manuscript consists of inverse problems for a coupled system of wave equations with potential in $\mathbb{R}^3$. By establishing the fundamental solution to the aforementioned operator, we study the uniqueness aspects of the…
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…
In this paper, we obtain the sharp uniqueness for an inverse $x$-source problem for a one-dimensional time-fractional diffusion equation with a zeroth-order term by the minimum possible lateral Cauchy data. The key ingredient is the unique…
In this article, we study an inverse boundary value problem for the time-dependent convection-diffusion equation. We use the nonlinear Carleman weight to recover the time-dependent convection term and time-dependent density coefficient…
We propose to solve inverse problems involving the temporal evolution of physics systems by leveraging recent advances from diffusion models. Our method moves the system's current state backward in time step by step by combining an…
This paper is concerned with time domain forward scattering and inverse scattering problems with a single moving point source as the emitter. Approximate solutions are provided for the forward scattering problem with a moving emitter.…
Diffusion with stochastic resetting, instantaneous returns of a diffusing particle to a reference point, creates a stationary probability distribution. The paradigm is extended here to a doubly stochastic protocol in which the resetting…