Related papers: On the Inverse Problem Relative to Dynamics of the…
This book aims to provide a brief overview of recent advancements in the theory of inverse problems for stochastic partial differential equations. In order to keep the content concise, we will only discuss the inverse problems of two…
This work belongs to the framework of inverse problems with linear model. The resolution of this type of problem consists in minimizing (possibly under constraints) a function of discrepancy between the measurements and a physical model of…
Inverse problems are concerned with the reconstruction of unknown physical quantities using indirect measurements and are fundamental across diverse fields such as medical imaging, remote sensing, and material sciences. These problems serve…
We consider the inverse problem for the dynamical system with discrete Schr\"odinger operator and discrete time. As an inverse data we take a \emph{response operator}, the natural analog of the dynamical Dirichlet-to-Neumann map. We derive…
The work studies some Difference equations, which are connected with Mejer's function.
This paper deals with the inverse problem of recovering an arbitrary number of fractional damping terms in a wave equation. We develop several approaches on uniqueness and reconstruction, some of them relying on Tauberian theorems on the…
We study inverse factorial series and their relation to Stirling numbers of the first kind. We prove a special representation of the polylogarithm function in terms of series with such numbers. Using various identities for Stirling numbers…
Dynamical inverse problem of representation theory, which has its origin in a classical paper of E.P.Wigner on a determination of commutation relations of quantum mechanical quantities by the quantum dynamical equations, is illustrated on…
Based on a Problem and its solution published on the pages of SIAM Review, we give an interesting integral representation for the Lambert $W$ function in this short note. In particular, our result yields a new integral representation for…
This paper focuses on an inverse problem associated with the plate equation which is derived from models in fluid mechanics and elasticity. We establish the unique identifying results in simultaneously determining both the unknown density…
We study the regularity of the distance function to the boundary of a domain in $\mathbb{R}^n$, with respect to the Minkowski functional of a convex polytope. We obtain the regularity of the distance function in certain cases. We also…
This work concerns the direct and inverse potential problems for the stochastic diffusion equation driven by a multiplicative time-dependent white noise. The direct problem is to examine the well-posedness of the stochastic diffusion…
We deal with the convergence of the value function of an approximate control problem with uncertain dynamics to the value function of a nonlinear optimal control problem. The assumptions on the dynamics and the costs are rather general and…
A Borg-Marchenko type uniqueness theorem (in terms of the Weyl function) is obtained here for the system auxiliary to the N-wave equation. A procedure to solve inverse problem is used for this purpose. The asymptotic condition on the Weyl…
A coefficient inverse problem for a parabolic equation is considered. Using a Carleman Weight Function, a globally strictly convex cost functional is constructed for this problem.
We apply the recently defined Lambert W function to some problems of classical statistical mechanics, i.e. the Tonks gas and a fluid of classical particles interacting via repulsive pair potentials. The latter case is considered both from…
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…
The paper is devoted to the development of the theory of inverse problems for evolution equations with terms rapidly oscillating in time. A new approach to setting such problems is developed for the case in which additional constraints are…
We establish simple connections between response functions of the dynamical Dirac systems and $A$-amplitudes and Weyl functions of the spectral Dirac systems. Using these connections we propose a new and rigorous procedure to recover a…
In this article, we study a direct and an inverse problem for the bi-wave operator $(\Box^2)$ along with second and lower order time-dependent perturbations. In the direct problem, we prove that the operator is well-posed, given initial and…