Magnetoencephalography (MEG) is a functional non-invasive modality which provides information on the temporal succession of cognitive processes with an excellent time resolution. Unfortunately, spatial resolution is limited due to the illposed nature of the MEG inverse problem for estimating source currents from the electromagnetic measurement. Therefore, prior information on the source current...

We exploit a recently developed nonlocal vector calculus to provide a variational analysis for a general class of nonlocal diffusion problems given by a linear integral equation on bounded domains in R. The ubiquity of the nonlocal operator is illustrated by a number of applications ranging from continuum mechanics to graph theory. These applications elucidate different interpretations of the o...

A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. By the space-time fractional diffusion equation we mean an evolution equation obtained from the standard linear diffusion equation by replacing the second-order space derivative with a Riesz-Fell...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 13 August 2020Accepted: 08 December 2020Published online: January 2021Keywordsfractional partial differential equations, inverse problems, Runge approximation propertyAMS Subject Headings35R11, 35R30Publication DataISSN (print): 0036-1410ISSN (online): 1095-7154Publisher:...

We have revisited the problem of anomalously diffusing species, modeled at the mesoscopic level using continuous time random walks, to include linear reaction dynamics. If a constant proportion of walkers are added or removed instantaneously at the start of each step then the long time asymptotic limit yields a fractional reaction-diffusion equation with a fractional order temporal derivative o...

In this paper, we study the forward and inverse problem for fractional magnetic Schrödinger equation with a nonlinear electric potential. We first obtain maximum principle linearized apply it to show that is well-posed under suitable assumptions exterior condition. Then uniqueness in recovering both potentials, assumed be analytic terms of solution, from data solution.

in many infeasible linear programs it is important to construct it to a feasible problem with a minimum pa-rameters changing corresponding to a given nonnegative vector. this paper defines a new inverse problem, called “inverse feasible problem”. for a given infeasible polyhedron and an n-vector a minimum perturba-tion on the parameters can be applied and then a feasible polyhedron is concluded.