+
RECENT RESULTS ON THE CAHN - HILLIARD EQUATION WITH DYNAMIC BOUNDARY CONDITIONS
стр.5-21
P. Colli, G. Gilardi, J. Sprekels
The pure or viscous Cahn - Hilliard equation with possibly singular potentials and dynamic boundary conditions is considered and the well-posedness of the related initial value problem is discussed. Then, a boundary control problem for the viscous Cahn -Hilliard system is studied and first order necessary conditions for optimality are shown. Moreover, the same boundary control problem is addressed for the pure Cahn - Hilliard system, by investigating it and passing to the limit in the analogous results for the viscous Cahn - Hilliard system as the viscosity coefficient tends to zero.
Загружаем данные из библиотечной системы...
Ключевые слова
+
MODELLING OF MECHANICAL SYSTEMS BASING ON INTERCONNECTED DIFFERENTIAL AND PARTIAL DIFFERENTIAL EQUATIONS
стр.22-34
The paper considers a boundary-value problem for a hybrid system of differential equations, which represents a generalized mathematical model for a system of interconnected rigid bodies attached to the rod by elastic-damping links. A hybrid system of differential equations is understood as a system of differential equations composed of ordinary differential equations and partial differential equations. For the theoretical foundations of our approach to investigation of the boundary value problem for the hybrid system of differential equations we propose a method of finding eigenvalues for the boundary-value problem. The comparative analysis of the results of numerical computations conducted with the use of the proposed method and the results obtained by other techniques known from the literature have proved the validity and the universal character of the proposed approach.
Загружаем данные из библиотечной системы...
Ключевые слова
+
OSCILLATION CRITERIA OF SECOND-ORDER NON-LINEAR DYNAMIC EQUATIONS WITH INTEGRO FORCING TERM ON TIME SCALE
стр.35-47
S.S. Negi, S. Abbas, M. Malik
This paper is concerned with the oscillatory properties of second order non-linear dynamic equation with integro forcing term on an arbitrary time scales. We reduce our original dynamic equation into an alternate equation by introducing a function of forward jump operator. To study oscillations we establish some crucial Lemmas and employ generalized Riccati transformation technique which transforms our second order dynamic equation into the first order dynamic equation on an arbitrary time scales. These results also guarantee that the solution of our equation oscillates. Furthermore, we establish the Kamenev-type oscillation criteria of our system. At the end, we consider a second order dynamic equation on time scales with deviating argument and compare it with our result which gives the sufficient conditions of oscillation of it.
Загружаем данные из библиотечной системы...
Ключевые слова
+
REGULARITY RESULTS AND SOLUTION SEMIGROUPS FOR RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS
стр.48-69
We show that the solutions of the retarded functional differential equations in a Banach space, whose existence and uniqueness are established in paper of A. Favini and H. Tanabe, have some further regularity properties if the initial data and the inhomogeneous term satisfy some smootheness assumptions. Some results on the solution semigroups analogous to the one of G. Di Blasio, K. Kunisch and E. Sinestrari and to the one of E. Sinestrari are also obtained.
Загружаем данные из библиотечной системы...
Ключевые слова
+
NEW RESULTS ON COMPLETE ELLIPTIC EQUATIONS WITH ROBIN BOUNDARY COEFFICIENT-OPERATOR CONDITIONS IN NON COMMUTATIVE CASE
стр.70-96
M. Cheggag, A. Favini, R. Labbas, S.Maingot, Kh.Ould Melha
In this paper, we prove some new results on operational second order differential equations of elliptic type with general Robin boundary conditions in a non-commutative framework. The study is performed when the second member belongs to a Sobolev space. Existence, uniqueness and optimal regularity of the classical solution are proved using interpolation theory and results on the class of operators with bounded imaginary powers. We also give an example to which our theory applies. This paper improves naturally the ones studied in the commutative case by M. Cheggag, A. Favini, R. Labbas, S. Maingot and A. Medeghri: in fact, introducing some operational commutator, we generalize the representation formula of the solution given in the commutative case and prove that this representation has the desired regularity.
Загружаем данные из библиотечной системы...
Ключевые слова
+
REAL SECTORIAL OPERATORS
стр.97-112
Sectorial operators that act in complex Banach spaces and map real subspaces into themselves should be called real sectorial operators. These operators have already been used implicitly in the study of various diffusion equations. Meanwhile, in the Lojasiewicz -Simon theory which provides longtime convergence of solutions to stationary solutions, the real valued Lyapunov functions play an important role. In order to make general methods for studying longtime convergence problems on the basis of the Lojasiewicz -Simon theory, it may therefore be meaningful to give an explicit definition for these real sectorial operators and to show their basic properties that are inherited from those of complex sectorial operators.
Загружаем данные из библиотечной системы...
Ключевые слова
+
BALTIC SEA WATER DYNAMICS MODEL ACCELERATION
стр.113-124
A.P. Bagliy, A.V. Boukhanovsky, B.Ya. Steinberg, R.B. Steinberg
Industrial Baltic sea water dynamics modelling program optimization and parallelization is described. Program is based on solving the system of partial differential equations of shallow water with numerical methods. Mechanical approach to program modernization is demonstrated involving building module dependency graph and rewriting every module in specific order. To achieve desired speed-up the program is translated into another language and several key optimization methods are used, including parallelization of most time-consuming loop nests. The theory of optimizing and parallelizing program transformations is used to achieve best performance boost with given amount of work. The list of applied program transformations is presented along with achieved speed-up for most time-consuming subroutines. Entire program speed-up results on shared memory computer system are presented.
Загружаем данные из библиотечной системы...
Ключевые слова
+
СТАЦИОНАРНЫЕ ТОЧКИ УРАВНЕНИЯ «РЕАКЦИЯ-ДИФФУЗИЯ» И ПЕРЕХОДЫ В СТАБИЛЬНЫЕ СОСТОЯНИЯ
стр.125-137
Рассмотрена бесконечномерная динамическая система, заданная уравнением «реакция-диффузия» с кубической нелинейностью при краевом условии Неймана и фиксированном значении средней величины. Изложена методика приближенного вычисления бифурцирующих решений при малых и конечных значениях закритичееко-го приращения параметра. Предложена также методика «трассировки» траекторий спуска из произвольного состояния (с произвольной концентрацией) в стабильное состояние (с концентрацией, реализующей минимум функционала энергии). Методика основана на вычислении сужения функционала энергии на линейную оболочку основных собственник функций (мод) оператора Лапласа и приближенном построении трассы спуска в виде последовательности точек, сопровождающих траекторию динамической системы. В случае малого закритического приращения бифуркационного параметра вычислены асимптотические представления бифурцирующих решений. В случае конечного закритического приращения бифуркационного параметра приведены примеры вычисления трассы спуска в точки минимума функционала энергии.
Загружаем данные из библиотечной системы...
Ключевые слова
+
МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ ЭРЕДИТАРНОГО ОСЦИЛЛЯТОРА ЭЙРИ С ТРЕНИЕМ
стр.138-148
Работа посвящена вопросам математического моделирования эредитарных колебательных систем с помощью математического аппарата дробного исчисления на примере осциллятора Эйри с трением. Модельное уравнение Эйри было записано в терминах дробных производных Герасимова - Капуто. Далее для этого обобщенного уравнения предложена конечно-разностная схема для численного счета. Рассмотрены вопросы аппроксимации, устойчивости и сходимости такой численной схемы. Приведены результаты моделирования, на основе численного решения построены осциллограммы и фазовые траектории в зависимости от различных значений управляющих параметров.
Загружаем данные из библиотечной системы...
Ключевые слова
+
COMPUTATIONAL EXPERIMENT FOR A CLASS OF MATHEMATICAL MODELS OF MAGNETOHYDRODYNAMICS
стр.149-155
A.O. Kondyukov, T.G. Sukacheva, S.I. Kadchenko, L.S. Ryazanova
The first initial-boundary value problem for the system modelling the motion of the incompressible viscoelastic Kelvin - Voigt fluid in the magnetic field of the Earth is investigated considering that the fluid is under external influence. The problem is studied under the assumption that the fluid is under different external influences depending not only on the coordinates of the point in space but on time too. In the framework of the theory of semi-linear Sobolev type equations the theorem of existence and uniqueness of the solution of the stated problem is proved.The solution itself is a quasi-stationary semitrajectory. The description of the problem’s extended phase space is obtained.The results of the computainal experiment are presented.
Загружаем данные из библиотечной системы...
Ключевые слова
+
TO THE 70TH ANNIVERSARY OF PROFESSOR ANGELO FAVINI
стр.156-158
Загружаем данные из библиотечной системы...
+
THE CONTRIBUTION OF ANGELO FAVINI IN TWENTY YEARS OF JOINT RESEARCH (1996 - 2016)
стр.159-164
Загружаем данные из библиотечной системы...
+
СЕМИНАРУ ПО УРАВНЕНИЯМ СОБОЛЕВСКОГО ТИПА ЧЕТВЕРТЬ ВЕКА
стр.165-169
Е.М. Буряк, Т.К. Плышевская, А.Б. Сатаров
Загружаем данные из библиотечной системы...
