Journal of Optimization, Differential Equations and their Applications (JODEA - Dnipro National Universuty) / Журнал з оптимізації, диференціальних рівнянь та їх застосувань
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ON SOME TYPES OF INVERSE PROBLEMS FOR DIFFERENTIAL EQUATIONS
Get PDFThe inverse problems for dierential equations are investigated, the solutionsof which do not use information about the exact characteristics of the physical process. Such inverse problems have not yet become widespread, but they are of great practical importance. Some approaches to solving inverse problems of this type are suggested
Uniform attractors for vanishing viscosity approximations of non-autonomous complex flows
Get PDFIn this paper we prove the existence of uniform global attractors in the strong topology of the phase space for semiflows generated by vanishing viscosity approximations of some class of non-autonomous complex fluids
ON A REPRESENTATION OF THE SOLUTION TO THE DIRICHLET PROBLEM IN A DISK. THE POISSON INTEGRAL BASED SOLUTION IN POLYNOMIALS
Get PDFThe representation u(x) = F2(x)Qm-2(x)+Qm(x) for the solution to the Dirichlet problem for the Laplace equation in a disk: F2(x) = jx - x0j2 - c2 6 0, is proved using the Poisson integral; Qm(x) being the polynomial boundary function of degree m, Qm-2(x) being the uniquely determined polynomial of degree m - 2
A Formulation of an Evolution Equation Governing Magnetic Lines
Get PDFIt is shown that `a free function' in the evolution equation of Hornig & Schindler for the magnetic induction (Physics of Plasmas, 3 (3), 781 - 791) has a unique representation, obtained in an explicit form. Some conclusions of the explicit formulation of the evolution equation are discussed
Optimal Control Problem for Some Degenerate Variation Inequality: Attainability Problem
Get PDFWe study an optimal control problem for degenerate elliptic variation inequality with degenerate weight function of potential type in the so-called class of H-admissible solutions. Using an appropriate regular algorithm of perturbation, we prove attainability of H-optimal pairs via optimal solutions of some non-degenerate perturbed optimal control problems
A CONTRIBUTION TO MAGNETIC RECONNECTION: A BOLTZMANN CORRECTION TO THE MAGNETIC INDUCTION EQUATION FOR FARADAY VORTEX TUBES
Get PDFThe Boltzmann correction to the Maxwell induction law for a moving mediumlled with vortex tubes of Faraday has been implemented
ON APPROXIMATION OF STATE-CONSTRAINED OPTIMAL CONTROL PROBLEM IN COEFFICIENTS FOR p-BIHARMONIC EQUATION
Get PDFWe study a Dirichlet-Navier optimal design problem for a quasi-linear mono-tone p-biharmonic equation with control and state constraints. The coecient of the p-biharmonic operator we take as a design variable in BV ( )\L1( ). In order to handle the inherent degeneracy of the p-Laplacian and the pointwise state constraints, we use regularization and relaxation approaches. We derive existence and uniqueness of solutions to the underlying boundary value problem and the optimal control problem. In fact, we introduce a two-parameter model for the weighted p-biharmonic operator and Henig approximation of the ordering cone. Further we discuss the asymptotic behaviour of the solutions to regularized problem on each ("; k)-level as the parameters tend to zero and innity, respectively
STEPS TO THE FUTURE
Get PDFHistorical milestones and directions of scientic research. To the 100th anniversaryof the Oles Honchar Dnipro National University and the 52nd anniversary of the Department of Dierential Equations
Про одне подання розв’язку задачi Дирихле для рiвняння Лапласа в крузi
No full textIt has been proven that the solution to the Dirichlet problem in a circle, wherethe boundary is specified as F2(x1; x2) = 0, F2(x1; x2) being a polynomial of degree 2, and the boundary function is specified as Qm(x1; x2), Qm(x1; x2) being a polynomial of degree m, admits representation u(x1; x2) = F2(x1; x2) PmДоказано, что решение задачи Дирихле в круге, на границе F2(x1, x2) = 0 которо- го задано условие в виде многочлена Qm(x1, x2) степени m, допускает однозначное пред- ставление u(x1, x2) = F2(x1, x2) Pm−2(x1, x2) + Qm(x1, x2), где Pm−2(x1, x2) — многочлен степени m − 2.Доведено, що розв’язок задачi Дирихле в крузi, на межi F2(x1, x2) = 0 якого задана умова у виглядi багаточлена Qm(x1, x2) степенi m, допускає однозначне подання u(x1, x2) = F2(x1, x2) Pm−2(x1, x2) + Qm(x1, x2), де Pm−2(x1, x2) — багаточлен степенi m − 2
Про регулярнiсть слабких розв’язкiв одного класу початково-крайових задач з псевдо-диференцiальними операторами
No full textWe discuss solvability and some extra regularity properties for the weak solutions toone class of the initial-boundary value problem arising in the study of the dynamicsof an arterial system.В роботе исследуется проблема разрешимости и вопросы регулярности слабых решений одного класса начально-краевых задач, возникающих при изучении динамики кардио-артериальных систем.В роботi дослiджується проблема розв’язанностi та питання регулярностi слабких розв’язкiв одного класу початково-крайових задач, якi описують динамiку кардiо-артерiальних систем