Registration Number
0214U007679,
0112U001205
, R & D reports
Title
Analytical and approximate methods for solving boundary value problems for differential equations in bounded and unbounded domains
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Head
Kalenyuk Petro Ivanovych, Доктор фізико-математичних наук
Registration Date
25-12-2014
Organization
Lviv Polytechnic National University
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We study the mixed problem for nonlinear evolution equation in unbounded domain in spatial variables. We prove the nonexistence of global solution in time variable of the solution of first mixed problem for a certain class of nonlinear evolution equations. We investigate boundary value problems with mixed conditions and problems with multipoint conditions in time for linear evolution equations and systems of equations in cylindrical domains. For linear hyperbolic equations of higher order with constant coefficients in a strip, we investigate the univalent solvability of the problem with Dirichlet-Neumann conditions in time variable and the periodicity or almost-periodicity conditions in spatial coordinate. We construct solutions in the form of series in the systems of orthogonal functions of spatial coordinates. For lower estimates of small denominators encountered when constructing the solutions, we used the metric approach. We investigate the correct solvability of the problem with local multipoint conditions in time for parabolic equation with Bessel operator in one of the spatial variables in a bounded domain, which is the Cartesian product of a torus and a rectangle. We give the results of investigating the hyperspaces of max-plus convex sets with the Vietoris topology in the non-compact and nonmetrized case. We establish the continuity of the mapping of max-plus convex shell in the Hausdorff metrics and the Vietoris topology; we prove the theorem on preserving the hyperspace of max-plus convex sets of Tikhonov cube by the functor. 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.5481
Product Description
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Іванець Надія Андріївна
Ільків Володимир Степанович
Базилевич Лідія Євгенівна
Баранецький Ярослав Омелянович
Бобик Ігор Омелянович
Волянська Ірина Ігорівна
Каленюк Петро Іванович
Когут Ігор Васильович
Мединський Ігор Павлович
Нитребич Зіновій Миколайович
Обшта Анатолій Феліксович
Пелех Ярослав Миколайович
Пташник Богдан Йосипович
Пукач Петро Ярославович
Сохан Петро Львович
Страп Наталя Ігорівна
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2020-04-02
