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Information × Registration Number 0211U007015, 0109U001157 , R & D reports Title Mixed problems and problems with conditions in selected variable for partial differential equations popup.stage_title Head Kalenyuk Petro Ivanovych, Доктор фізико-математичних наук Registration Date 16-03-2011 Organization Lviv Polytechnic National University popup.description2 We investigate mixed problems for nonlinear differential equations modelling important processes in the inhomogeneous media in unbounded domains; study problems with integral conditions for hyperbolic and typeless partial differential equations in cylindric domains; establish the univalent solvability of the problems, investigate the smoothness of the solutions and continuous dependence on the right-hand sides of the conditions and the equations; construct the perturbations operators of linear differential equations which leave the point spectrum unchanged, investigate the properties of the solutions of the problems obtained as a result of perturbation; investigate the problems with two multiple nodes for the factirized equations with constant coefficients in a bounded domain. The research has been carried out by means of the Galerkin method, the monotonicity method, the compactness method, the Fourier method (generalized separation of variables), the spectral method, the isospectral perturbations method, the metrical approach to the studying of small denominators, the isomorphism of spaces. We use the methods of the metrical theory of Diophantine approximations, the method of depletion of unbounded domain by the sequence of bounded domains with a certain extensions of the initial data and the solution. The results have been implemented while developing some special courses for students of the universities as well as for mathematical modelling the important physical processes in nonhomogeneous media. Product Description popup.authors Іванець Надія Андріївна Ільків Володимир Степанович Баранецький Ярослав Омелянович Бобик Ігор Омелянович Каленюк Петро Іванович Когут Ігор Васильович Магеровська Тетяна Валеріївна Машталір Тетяна Ярославівна Нитребич Зіновій Миколайович Пелех Ярослав Миколайович Пташник Богдан Йосипович Пукач Петро Ярославович Слюсарчук Арсен Юрійович Сохан Петро Львович Ярка Уляна Борисівна popup.nrat_date 2020-04-02 Close