Related papers: Recovery of rapidly decaying source terms from dyn…
This paper considers the inverse problem of recovering state-dependent source terms in a reaction-diffusion system from overposed data consisting of the values of the state variables either at a fixed finite time (census-type data) or a…
We revisit the notion of reduced spectra $sp_{\Cal {F}} (\phi)$ for bounded measurable functions $\phi \in L^{\infty} (J,\Bbb{X})$, ${\Cal {F}}\subset L^1_{loc}(J,\Bbb{X})$. We show that it can not be obtained via Carleman spectra unless…
In this article we study inverse problems of recovering a space-time dependent source component from the lateral boundary observation in a subidffusion model. The mathematical model involves a Djrbashian-Caputo fractional derivative of…
This paper is concerned with inverse source problems for the acoustic wave equation in the full space R^3, where the source term is compactly supported in both time and spatial variables. The main goal is to investigate increasing stability…
In this paper, we investigate the inverse problem on determining the spatial component of the source term in a hyperbolic equation with time-dependent principal part. Based on a newly established Carleman estimate for general hyperbolic…
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 employ the superpotential technique for the reconstruction of cosmological models with a non-minimally coupled scalar field evolving on a spatially flat Friedmann-Robertson-Walker background. The key point in this method is that the…
We consider fractional diffusion-wave equations with source term which is represented in a form of a product of a temporal function and a spatial function. We prove the uniqueness for inveres source problem of determining spatially varying…
We consider the question of exponential decay to equilibrium of solutions of an abstract class of degenerate evolution equations on a Hilbert space modeling the steady Boltzmann and other kinetic equations. Specifically, we provide…
In this paper, we investigate two inverse source problems for degenerate time-fractional partial differential equation in rectangular domains. The first problem involves a space-degenerate partial differential equation and the second one…
We present and analyze a novel sparse polynomial technique for approximating high-dimensional Hilbert-valued functions, with application to parameterized partial differential equations (PDEs) with deterministic and stochastic inputs. Our…
This paper studies an inverse source problem for a viscoelastic membrane, where the material's memory effect is characterized by the Riemann-Liouville fractional derivative. The problem is to recover the unknown source term from the limited…
The conjugate phase retrieval problem concerns the determination of a complex-valued function, up to a unimodular constant and conjugation, from its magnitude observations. It can also be considered as a conjugate phaseless sampling and…
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…
A compact expression for the DeWitt-Schwinger renormalization terms suitable for use in even-dimensional space-times is derived. This formula should be useful for calculations of $<\phi^2(x)>$ and $<T_{\mu\nu}(x)>$ in even dimensions.
The dynamical sampling problem is centered around reconstructing signals that evolve over time according to a dynamical process, from spatial-temporal samples that may be noisy. This topic has been thoroughly explored for one-dimensional…
Phase retrieval arises in various fields of science and engineering and it is well studied in a finite-dimensional setting. In this paper, we consider an infinite-dimensional phase retrieval problem to reconstruct real-valued signals living…
In this paper, we consider the prediction of the helium concentrations as function of a spatially variable source term perturbed by fractional Brownian motion. For the direct problem, we show that it is well-posed and has a unique mild…
In this work, we study the inverse problem of recovering a potential coefficient in the subdiffusion model, which involves a Djrbashian-Caputo derivative of order $\alpha\in(0,1)$ in time, from the terminal data. We prove that the inverse…
We consider bounded operators $A$ acting iteratively on a finite set of vectors $\{f_i : i\in I\}$ in a Hilbert space $\mathcal H$ and address the problem of providing necessary and sufficient conditions for the collection of iterates…