Inverse problems and stochastic methods research group

Research classification (Frascati)
Head of the research group
Keyword
inverse problems
fractional diffusion and wave motion
direct and inverse scattering
nonparametric statistics
Overview
The main directions of research are:‚ Inverse problems for equations containingfractional derivatives. Inverse problemsfor linear and nonlinear fractional differential equations are studied. The unknowns to be determined are coefficients,source terms and kernels of generalizedfractional time derivatives. Such problemsoccur in modelling of diffusion and mechanical processes in porous, fractal andbiological media. The research is focusedon both theoretical aspects and elaborationof numerical methods.‚ Direct and inverse scattering in singularand nonlocal media. Electromagnetic andacoustic direct and inverse scatteringin media with singularities or non-localfeatures is studied. Mathematical theory of tripole and more general multipoleantennas is developed. This branch iscomplemented by a development of newsignal processing on state-of-the-art computational methods for large-scale inverseproblems. Inverse problems to reconstructin homogeneities of media with non-localproperties by means of measurements ofscattered acoustic waves at boundariesare investigated.‚ Elaboration of nonparametric statisticalmethods. The theory of nonparametricstatistical methods is developed and thesemethods are applied in environmental andbuilding engineering.
Important results
Main results of 2021:‚ We proved that an energy of a far-fieldpattern scatted from a corner has alwaysa positive lower bound. This implies theimpossibility of invisibility cloaking of anobject with corners.‚ We proved that a solution of the fractionaldiffusion-wave equation can be uniquelyrestored by means of final data providedboundary conditions are given in an arbitrarily small neighborhood of the finalvalue.
Period of activity of the research group
Related department
Department of cybernetics
Publications related to the research group