The Uniqueness of the Solution for the First Initial-Boundary Value Problem for Parabolic Systems on the Plane in the Model Case

2018 ◽  
Vol 483 (3) ◽  
pp. 241-243
Author(s):  
E. Baderko ◽  
◽  
M. Cherepova ◽  
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Parabolic Systems ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Model Case ◽  
Uniqueness Of The Solution ◽  
Initial Boundary Value

scholarly journals Correctness investigation for the suspension transport problem in coastal systems

2018 ◽  
Vol 226 ◽  
pp. 04027 ◽  
Author(s):  
Alexander I. Sukhinov ◽  
Valentina V. Sidoryakina ◽  
Sofya V. Protsenko
Keyword(s):  
Boundary Value Problem ◽  
Water Movement ◽  
Boundary Value ◽  
Three Dimensional ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Solution Stability ◽  
Three Dimensional Model ◽  
Uniqueness Of The Solution ◽  
Initial Boundary Value

This article is devoted to the confirmation the need for using a set of 3D dynamics models describing the various hydrophysical characteristics of the studied object to solve practical problems associated with the assessment of the ecological state of the water reservoirs. The present paper is devoted to the study of the three-dimensional model of transport and sedimentation of suspended matter in the coastal zone. The model takes into account such parameters as water movement, diffusionconvection, complicated bottom and shoreline geometry, lifting, transport and sedimentation of slurry. The existence and uniqueness of the solution of the corresponding indicated model of the initial-boundary value problem haas been envestigateded for two typical bottom boundary condirions. Also solution stability of the boundary-value problem in depend of functions: initial condition, boundary conditions and the righthand side in the norm L2 for any moment of time 0 < T < +∞, and also in the time-integral norm L2 has been proved. The model may be basis for the construction of hydrophysics models used to describe processes in the extraction of minerals from the seabed, in the dissemination of suspensions in shelf regions.

RESEARCH OF THE IMPACT DEVICE MODEL OF THE ROD TYPE BY DIFFERENCE METHOD

2020 ◽  
pp. 73-80
Author(s):  
А.М. Слиденко ◽  
В.М. Слиденко
Keyword(s):  
Boundary Value Problem ◽  
Difference Method ◽  
Model Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Cross Sectional ◽  
Impact Device ◽  
Initial Boundary Value ◽  
The Impact

Приводится анализ механических колебаний элементов ударного устройства с помощью модели стержневого типа. Ударник и инструмент связаны упругими и диссипативными элементами, которые имитируют их взаимодействие. Аналогично моделируется взаимодействие инструмента с рабочей средой. Сформулирована начально-краевая задача для системы двух волновых уравнений с учетом переменных поперечных сечений стержней. Площади поперечных сечений определяются параметрическими формулами при сохранении объемов стержней. Параметрические формулы позволяют получать различного вида зависимости площади поперечного сечения стержня от его длины. Начальные условия отражают физическую картину взаимодействия инструмента с ударником и рабочей средой. Краевые условия описывают контактные взаимодействия ударника с инструментом и последнего с рабочей средой. В качестве модельной задачи рассматривается соударение ударника и инструмента через элемент большой жесткости. Начально-краевая задача исследуется разностным методом. Проводится сравнение решений задачи, полученных с помощью двухслойной и трехслойной разностных схем. Такие схемы реализованы в общей компьютерной программе в системе Mathcad. Показано, что при вычислениях распределения нормальных напряжений по длине стержня лучшими свойствами относительно устойчивости обладает двухслойная схема The article gives the analysis of mechanical vibrations of the impact device elements using the model of the rod type. The hammer and the tool are connected by elastic and dissipative elements that simulate their interaction. The interaction of the tool with the processing medium is simulated in a similar way. An initial boundary-value problem is formulated for a system of two wave equations taking into account the variable cross sections of the rods. Cross-sectional areas are determined by parametric formulas maintaining the volume of the rods. Parametric formulas allow one to obtain various dependence types of the cross-sectional area of the rod on its length. The initial and boundary conditions reflect the physical phenomenon of the tool interaction with the processing medium, and also describe the contact interactions of the hammer with the tool. The impacting of the hammer and the tool through an element of high rigidity is considered as a model problem. To control the limiting values, the solution of the model problem by the Fourier method is used. The initial-boundary-value problem is investigated by the difference method. A comparison of solutions obtained for the two-layer and three-layer difference schemes is given. Such schemes are realized in a common computer program in the Mathcad. It is shown that the two-layer scheme has the best properties in relation to stability while calculating the distribution of normal voltage along the length of the rod

scholarly journals Initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Liming Xiao ◽  
Mingkun Li
Keyword(s):  
Weak Solution ◽  
Boundary Value Problem ◽  
Parabolic Equations ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Higher Order ◽  
Evolution Problem ◽  
Positive Energy ◽  
Initial Boundary Value

AbstractIn this paper, we study the initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations which do not have positive energy and come from the soil mechanics, the heat conduction, and the nonlinear optics. By the mountain pass theorem we first prove the existence of nonzero weak solution to the static problem, which is the important basis of evolution problem, then based on the method of potential well we prove the existence of global weak solution to the evolution problem.

Sign in / Sign up

Export Citation Format

Share Document