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We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…

We study the inverse problem of recovering a spatially dependent variable order in a time-fractional diffusion model from the boundary flux measurement generated by a single boundary excitation. It arises in the identification of…

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 work, we investigate the shape identification and coefficient determination associated with two time-dependent partial differential equations in two dimensions. We consider the inverse problems of determining a convex polygonal…

In this paper, we study several inverse problems associated with a fractional differential equation of the following form: \[ (-\Delta)^s u(x)+\sum_{k=0}^N a^{(k)}(x) [u(x)]^k=0,\ \ 0<s<1,\ N\in\mathbb{N}\cup\{0\}\cup\{\infty\}, \] which is…

In this paper, we propose and study several inverse problems of identifying/determining unknown coefficients for a class of coupled PDE systems by measuring the average flux data on part of the underlying boundary. In these coupled systems,…

Examples of axially symmetric solutions to Einstein's field equations are given that exhibit anomalous "negative frame dragging" in the sense that zero angular momentum test particles acquire angular velocities in the opposite direction of…

In this article, we study the one-dimensional inverse problem of determining the memory kernel by the integral overdetermination condition for the direct problem of finding the velocity potential and the displacement of boundary points. A…

We consider possible generation of singularities of a vector field transported by diffeomorphisms with derivatives of uniformly bounded determinants. A particular case of volume preserving diffeomrphism is the most important, since it has…

In geophysics, inverse modelling can be applied to a wide range of goals, including, for instance, mapping the distribution of rock physical parameters in applied geophysics and calibrating models to forecast the behaviour of natural…

An inverse scattering problem for the 3D acoustic equation in time domain is considered. The unknown spatially distributed speed of sound is the subject of the solution of this problem. A single location of the point source is used. Using a…

This paper is concerned with the forward and inverse problems for the fractional semilinear elliptic equation $(-\Delta)^s u +a(x,u)=0$ for $0<s<1$. For the forward problem, we proved the problem is well-posed and has a unique solution for…

We consider a mathematical model related to reconstruction of cardiac electrical activity from ECG measurements on the body surface. An application of recent developments in solving boundary value problems for elliptic and parabolic…

We consider the motion of the interface separating two domains of the same fluid that moves with different velocity along the tangential direction of the interface. We assume that the fluids occupying the two domains are of constant…

This paper is addressed to an inverse stochastic hyperbolic equation with three unknowns, i.e., a source term, an initial displacement and an initial velocity. The global uniqueness is proved by a new global Carleman estimate for the…

Variable order differential equations with non-integrable singularities are considered on spatial networks. Properties of the spectrum are established, and the solution of the inverse spectral problem is obtained.

We consider the problem of reconstruction of the Cauchy data for the wave equation in $\mathbb{R}^3$ and $\mathbb{R}^2$ by the measurements of its solution on the boundary of the unit ball.

An inverse problem of wave propagation into a weakly laterally inhomogeneous medium occupying a half-space is considered in the acoustic approximation. The half-space consists of an upper layer and a semi-infinite bottom separated with an…

In a variety of scientific applications we wish to characterize a physical system using measurements or observations. This often requires us to solve an inverse problem, which usually has non-unique solutions so uncertainty must be…

To understand the mechanics of a complex fluid such as a foam we propose a model experiment (a bidimensional flow around an obstacle) for which an external sollicitation is applied, and a local response is measured, simultaneously. We…