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A functional analytic approach for the analysis of nonlinear transmission problems
Research AreaH2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility
Project ReferenceH2020-MSCA-IF-2014-654795-FAANon
CoordinatorProfessor Gennady S. Mishuris
Project Funding195 454,8 euro
ResearcherDr Matteo Dalla Riva
Contract TypeMarie Sklodowska-Curie Individual Fellowship (IF)
Start Date2015-12-01
Duration24 months
Project Description The purpose of the research plan is the development of the method called Functional Analytical Approach (FAA) for the analysis of singular perturbations of nonlinear transmission problems. The techniques proposed are based on potential theory and functional analysis and aim at describing the effect of perturbations in terms of real analytic functions. Both perturbations of the shapes of the domains of definition and of the coefficients of the operators will be considered. A special attention will be paid to the case of perforated and periodically perforated domains with shrinking holes and inclusions. The problems addressed are of interest also in view of inter-sectorial applications to the analysis of physical models in fluid dynamic, in elasticity, and in thermodynamic. Concrete applications will be shown in the study effective properties of composite materials, in inverse problems in acoustic and electromagnetic scattering, and in inclusion detection problems. The final goal within the action is the realisation of a complete theory based on the FAA which will represent in future a key tool for the analysis of perturbed boundary value problems.