Количество страниц: 16 с.
The article is devoted to studying one of the sections of nonclassical differential equations, namely, matters concerned with solvability of parabolic equations with changing second-order time direction. As is known, in ordinary boundary-value problems for strictly parabolic equations, the smoothness of the initial and boundary conditions completely ensures that the solutions belong to the Holder spaces, but in the case of equations with changing time direction, the smoothness of the initial and boundary conditions does not ensure that the solutions belong to these spaces. S.A. Tersenov (for a model parabolic equation with changing time direction) and S.G. Pyatkov (for a more general second-order equation) obtained the necessary and sufficient conditions for solvability of the corresponding mixed problems in Holder spaces. In so doing, they always assumed the initial and boundary conditions being equal to zero. Cases in which the initial and boundary conditions belong to Banach spaces are considered. The functional spaces in which the solutions must be sought are introduced. Relevant a priori estimates, which make it possible to obtain the solvability conditions for these problems, are obtained. The properties of the obtained solutions have been studied. In particular, the equivalence of the Riesz and Littlewood-Paley conditions similar to the conditions for solutions of strictly elliptic and strictly parabolic second order equations is established. A unique solvability of the first mixed problem with boundary and initial functions from the Banach space has been proved.
Петрушко, И. М. О первой смешанной задаче в банаховых пространствах для вырождающихся уравнений с меняющимся направлением времени / И. М. Петрушко, М. И. Петрушко // Математические заметки СВФУ. — 2018. — Т. 25, N 4 (100), октябрь-декабрь. — С. 45-59.
DOI: 10.25587/SVFU.2018.100.20553
Количество страниц: 12 с.
Кожанов, А. И. Краевые задачи для дважды вырождающегося дифференциального уравнения с кратными характеристиками / А. И. Кожанов, О. С. Зикиров // Математические заметки СВФУ. — 2018. — Т. 25, N 4 (100), октябрь-декабрь. — С. 34-44.
DOI: 10.25587/SVFU.2018.100.20552
Количество страниц: 20 с.
We establish the necessary and sufficient conditions for the solution of the second-order parabolic equation in a stellar domain with a lateral boundary in the class degenerate on the boundary of the domain, to have an average limit on the lateral surface of the cylindrical domain and the limit in the mean on its lower base. Also, we study the unique solvability of the first mixed problem for such equations in the case when the boundary and initial functions belong to spaces of the type. The closest to the questions under consideration are the theorems of Riesz and Littlewood and Paley, in which criteria are given for the limit values in p > 1, of functions analytic in the unit disk. Further development of this topic for uniformly elliptic equations was obtained in the works V. P. Mikhailov and A. K. Gushchin. The boundary smoothness condition can be weakened, as was shown by I. M. Petrushko. Under the weakest restrictions on the smoothness of the boundary (and on the coefficients of the equation), the criteria for the existence of a boundary value were established in by A. K. Gushchin. In this case, all directions of the acceptance of boundary values for uniformly elliptic equations turn out to be equal, the solution has the property similar to the property of continuity with respect to the set of variables. In the case of degeneracy of the equation on the boundary of the domain, when the directions are not equal, the situation is more complicated. In this case, the formulation of the first boundary value problem is determined by the type of degeneracy. When the values of the corresponding quadratic form of the degenerate elliptic equation on the normal vector are different from zero (Tricomi type degeneracy), the Dirichlet problem is well-posed and the properties of such degenerate equations are very close to the properties of uniformly elliptic equations. In particular, in this situation analogues of the Riesz and Littlewood-Paley theorems are valid.
Капицына, Т. В. О существовании граничных и начальных значений для вырождающихся параболических уравнений в звездных областях / Т. В. Капицына // Математические заметки СВФУ. — 2018. — Т. 25, N 4 (100), октябрь-декабрь. — С. 15-33.
DOI: 10.25587/SVFU.2018.100.20551
Количество страниц: 12 с.
In the Sobolev spaces, we consider the well-posedness questions for the inverse problem of recovering the source function of a mixed type equation of second order. The overdetermination conditions are the values of a solution on a collection of planes of dimension n − 1. The unknowns occurring in the right-hand side depend on time and n − 1 unknown space variables. Under certain natural conditions on the data of the problem, we obtain existence and uniqueness theorems for generalized solutions to this problem. The conditions on the data almost coincide with those ensuring solvability of the direct problem. The parameter continuation method and a priori estimates are used to validate the results. The method allows us to generalize the results to the case of smoother data and regular solutions.
Джамалов, С. З. Некоторые классы обратных задач для уравнений смешанного типа второго порядка / С. З. Джамалов, С. Г. Пятков // Математические заметки СВФУ. — 2018. — Т. 25, N 4 (100), октябрь-декабрь. — С. 3-14.
DOI: 10.25587/SVFU.2018.100.20550
Количество страниц: 6 с.
- Математика. Естественные науки > Математика,
- НАУКА ЯКУТИИ > МАТЕМАТИКА. ЕСТЕСТВЕННЫЕ НАУКИ > Математика,
- Прикладные науки. Медицина. Ветеринария. Техника. Сельское хозяйство > Инженерное дело. Техника в целом,
- НАУКА ЯКУТИИ > МАТЕМАТИКА. ЕСТЕСТВЕННЫЕ НАУКИ > Физика,
- НАУКА ЯКУТИИ > ПРИКЛАДНЫЕ НАУКИ. МЕДИЦИНА. ТЕХНИКА. СЕЛЬСКОЕ ХОЗЯЙСТВО > Инженерное дело. Техника в целом.
This paper considers a mathematical model of joint laying of water pipeline networks and district heat networks. The purpose of the work is to study the effect of radiation on the process of complex heat exchange taking place in the housing insulation between structural elements. The results of mathematical simulation of the heat loss taking into account the radiant component are given. When calculating the heat flows which are lost in the pipeline through thermal insulation at transporting the coolant, the heat transfer process is usually considered by means of conduction and convection. The radiant component is neglected in most cases. The influence of heat transfer by radiation and convection is particularly noticeable using thermal insulation products with large pores and air gaps. A ground configuration of a pipe line and water pipe line laid in a joint thermal insulation made of mineral wool is considered. When laying joint pipelines, complex radiative heat transfer occurs. It consists, for each one of these pipelines, of radiation reflected from the other pipeline and self-radiation. A non-stationary temperature field of the structure, consisting of two parallel stacked pipes with different diameters lying in a joint insulating structure made of mineral wool, is calculated. The construction elements exchange heat with each other and the environment by convection and radiation.
Степанов, А. В. Оценка влияния лучистой составляющей на сложный теплообмен между сетевым трубопроводом и водопроводом при совместной прокладке / А. В. Степанова, Г. Н. Егорова // Наука и образование. — 2017. — N 4 (88), октябрь-декабрь. — С. 93-98.
Количество страниц: 5 с.
The influence of solar radiation in the temperature field of the permafrost massif on horizontal surfaces is considered taking into account changes in solar radiation during the day. A mathematical process model is constructed and implemented based on a Stefan type problem. The calculation of the number of freezing-thawing cycles in the spring and autumn for the conditions of Central Yakutia was made.
Расчет количества циклов замерзания-оттаивания породного массива для условий центральной Якутии на горизонтальных поверхностях / В. И. Слепцов, С. Д. Мордовской, Е. Е. Петров. – Текст : непосредственный // Горный информационно-аналитический бюллетень. – 2012. – N 9. – C. 99-114.
Ответственность: Борисов Парфений Прокопьевич (Автор обозрения, рецензии), Филиппова Нина Игнатьевна (Редактор)
Издательство: Якутский край
Год выпуска: 2007
Количество страниц: 60 с.
- Саха тыла/Якутский язык > Учебные издания > Школьникам, педагогам,
- Саха тыла/Якутский язык > Словари > Терминологические словари,
- Языки народов Якутии > Якутский язык > Словари > Терминологические словари,
- Языки народов Якутии > Якутский язык > Учебные издания > Школьникам, педагогам,
- Общий отдел > Справочные издания общего типа. Энциклопедии. Словари,
- Математика. Естественные науки > Математика,
- Языкознание. Филология. Художественная литература > Языкознание и языки. Лингвистика > Якутский (саха),
- НАУКА ЯКУТИИ > МАТЕМАТИКА. ЕСТЕСТВЕННЫЕ НАУКИ > Математика,
- НАУКА ЯКУТИИ > ЯЗЫКОЗНАНИЕ. ФИЛОЛОГИЯ. ЛИТЕРАТУРОВЕДЕНИЕ. ХУДОЖЕСТВЕННАЯ ЛИТЕРАТУРА > Языкознание и языки. Лингвистика,
- НАУКА ЯКУТИИ > ОБЩИЙ ОТДЕЛ > Справочные издания общего типа. Энциклопедии, словари,
- ШКОЛА > Школьнику > Математика,
- ШКОЛА > Педагогу > Преподавание дисциплин > Математика,
- Школа 2 > Предметные подборки > Математика,
- Школа 2 > Предметные подборки > Справочная литература > Словари.
Винокурова, М. Е. Русско-якутский терминологический словарь по математике для начальных классов / М. Е. Винокурова. – Якутск : Якутский край, 2007. – 55 с.
Количество страниц: 10 с.
The initial form of the grains of gold found in the nature in most cases is a flat plate (a scaly form). However, during pneumoseparation, the toroidal shape of pieces of gold is often found and considered to be the most effective. Thus the task of estimating time of formation of a toroidal piece of gold is important. In the paper, we consider the evolution of the surface of a flat disk of malleable metal deformed by isotropic bombing with fine particles and develop a mathematical model of this evolution. We obtain a differential equation describing the change of the deformed surface of a round disk which is solved then by a Runge–Kutta method. Studying the solution of the equation, we found that the body rather quickly reaches the most stable toroidal form when the deformed surface gets its maximal value and then a slower transformation of the surface into the sphere follows. We estimate the time of formation of a toroid from a disk with certain parameters of the considered system. The received results could be used for developing more exact models of evolution of flat bodies bombed with fine particles. Keywords: mathematical model, differential equation, deformed surface, toroid, enrich.
Моделирование динамики формы плоского тела из ковкого металла при изотропной бомбардировке частицами песка / А. И. Матвеев, Д. А. Осипов, Д. Р. Осипов, Б. В. Яковлев. – Текст : непосредственный // Математические заметки СВФУ. – 2017. – Т. 24, N 1 (93) январь-март. – C. 99-108.
Количество страниц: 7 с.
- Математика. Естественные науки > Математика,
- Прикладные науки. Медицина. Ветеринария. Техника. Сельское хозяйство > Инженерное дело. Техника в целом > Горное дело. Горные предприятия (рудники, шахты, карьеры),
- НАУКА ЯКУТИИ > МАТЕМАТИКА. ЕСТЕСТВЕННЫЕ НАУКИ > Математика,
- НАУКА ЯКУТИИ > ПРИКЛАДНЫЕ НАУКИ. МЕДИЦИНА. ТЕХНИКА. СЕЛЬСКОЕ ХОЗЯЙСТВО > Инженерное дело. Техника в целом > Горное дело. Горные предприятия (рудники, шахты, карьеры).
Математическое моделирование процесса концентрации тяжелых частиц в постели отсадочной машины / Е. С. Слепцова, Л. В. Никифорова, Б. В. Яковлев, А. И. Матвеев // Горный информационно-аналитический бюллетень. – 2014. – N 10. – C. 239-245.
Количество страниц: 7 с.
- Математика. Естественные науки > Математика,
- Прикладные науки. Медицина. Ветеринария. Техника. Сельское хозяйство > Инженерное дело. Техника в целом > Горное дело. Горные предприятия (рудники, шахты, карьеры),
- НАУКА ЯКУТИИ > МАТЕМАТИКА. ЕСТЕСТВЕННЫЕ НАУКИ > Математика,
- НАУКА ЯКУТИИ > ПРИКЛАДНЫЕ НАУКИ. МЕДИЦИНА. ТЕХНИКА. СЕЛЬСКОЕ ХОЗЯЙСТВО > Инженерное дело. Техника в целом > Горное дело. Горные предприятия (рудники, шахты, карьеры).
One of efficient methods to separate heavy grains from granular material, for instance, gold, is gravity jigging. The known approaches to jigging modeling use the Brownian particle theory and solve the Fokker-Planck equation. The interaction between particles of useful fraction is neglected in this case. The present article is focused on determination of parameters which take into account such interaction. The theoretically modeled parameters are later on found experimentally. The test material is chosen to be magnetic substance contained in natural sand. This material (heavy particles) have higher density than sand (by a factor of 1.2 approximately). The heavy particles are separated from sand using permanent magnet. As result of the research, theoretical distributions of the magnetic substance concentrations along the height of a test container are obtained and adapted to experimental data. The tests are carried out in varied conditions: dry mix, liquid mix, varied vibration regimes. The resultant distributions, given the preset initial conditions (e.g. definite percentage of heavy particles and total sand volume), enable calculating time of formation of a preset material layer with the certain concentration of useful fraction on the bottom of the settlement container. The research findings show that the gradient force grows in time while the medium resistance decreases vice versa in case that all useful fraction (heavy particles) is at the top of the sand contained at the initial time
Исследование распределения тяжелых фракций в колеблющейся сыпучей среде / Е. С. Слепцова, Б. В. Яковлев, А. И. Матвеев. – Текст : непосредственный // Горный информационно-аналитический бюллетень. – 2018. – N 9. – C. 186-192.