ОБЕРНЕНI КОЕФIЦIЄНТНI ЗАДАЧI КОМПЕТИТИВНОЇ ДИФУЗIЇ В НЕОДНОРIДНИХ СЕРЕДОВИЩАХ НАНОПОРИСТИХ ЧАСТИНОК З ВИКОРИСТАННЯМ ҐРАДIЄНТНИХ МЕТОДIВ
Abstract
Розглядається обернена коефiцiєнтна задача для компетитивної дифузiї в неоднорiдних середовищах нанопористих частинок. Здiйснено постановка та об рунтуванням прямої та спряженої крайових задач та побудовано їх розв'язки операцiйним методом Гевiсайда. Отримано явнi вирази градiєнтiв функцiоналiв-нев'язок для iдентифiкацiї параметрiв нанопористих середовищ, при допомозi яких вiдновлено розподiли коефiцiєнтiв дифузiї для intercrystallytes та intracrystallytes просторiв як функцiй вiд часу для рiзних положень частинок в середовищi. Змодельовано розподiли концентрацiй двох дифундованих компонентiв в дослiджуваному наносередовищi
Inverse problem for coefficients finding of competitive diffusion in heterogeneous media of nanoporous particles has been considered. Formulation and justification of direct and conjugate boundary problems has been provided. The solutions of boundary problems has been build taking advantage of Heaviside's methods. Explicit expressions for gradients functional residuals has been obtained to identify the parameters of nanoporous media in form of diffusion coefficients for intercrystallytes and intracrystallytes spaces as functions of time for different modes of particles along the catalyst layer. Distributions of concentrations for two defunded components in studied sample of nanoporous media has been visualized.
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