Registration Number
0214U000068,
0111U000481
, R & D reports
Title
Local, global and asymptotic properties of solutions of singular, spectral and nonclassical problems for elliptic and evolution equations and variational inequalities
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Head
Kovalevsky Alexander Al'bertovich, Shishkov Andrey Evgenievich,
Registration Date
15-01-2014
Organization
Institute of Applied Mathematics and Mechanics of National Academy of Sciences of Ukraine
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Theorems on the boundedness of solutions for a large class of degenerate anisotropic elliptic variational inequalities of second-order are proved. Global boundedness is established under the condition of a certain regularity of the right-hand sides of the variational inequalities under consideration, and it is shown that in general this condition can not be improved in the scale of Lebesgue spaces. The Dirichlet problem is studied in a bounded multidimensional domain for semilinear elliptic equations with absorbing potentials degenerated on some subsets of the domain. Exact necessary and sufficient conditions on the character of the given degeneration which guarantee existence or nonexistence of "large" and supersingular solutions are established. The Cauchy-Neumann problem with finite initial data is investigated for degenerate quasilinear parabolic equations like the equation of the flow of thin capillary films. Exact estimates from above on the initial distribution of the supports, depending on asymptotic behaviour of the initial function in the neighbourhood of the boundary of its support, are established. All range of possible asymptotics is considered from critical small one, guaranteeing the effect of a temporary delay of distribution, to singular one like Dirac delta-function. We consider the question on the uniqueness of a solution to the Dirichlet problem for the equation of string oscillation which is equivalent to well known classical problems in geometry, algebra and analysis. By means of analogy to the Ritta problem, we find domains for which the uniqueness of a solution to the Dirichlet problem is described by the condition of rationality of some number which is calculated according to the data of the problem. We investigate absolutely continuous, singular and point spectrum of the one-dimensional Dirac operator with infinite number of point interactions. Self-conjugacy of such operators on an infinite interval is proved.
Product Description
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Бурський Володимир Петрович
Войтович Михайло Володимирович
Зарецька Ганна Олександрівна
Каліта Євген Олександрович
Карабаш Ілля Михайлович
Лесіна Євгенія Вікторівна
Мірошникова Анастасія Анатоліївна
Маламуд Марк Михайлович
Намлєєва Юлія Валеріївна
Рудакова Ольга Анатоліївна
Степанова Катерина Вадимівна
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2020-04-02
