A Problem with Mixed Boundary Conditions for a Singular Elliptic Equation in an Infinite Domain

Ergashev, Tuhtasin; Tulakova, Z. R.

doi:10.3103/s1066369x22070039

Russ Math.

2022

DOI: 10.3103/s1066369x22070039

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A Problem with Mixed Boundary Conditions for a Singular Elliptic Equation in an Infinite Domain

Tuhtasin Ergashev

Z. R. Tulakova²

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Cited by 5 publications

References 13 publications

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About one differential model of dynamics of groundwater

Abdullayev,

Hidoyatova,

Kuralov

2023

E3S Web of Conf.

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When modeling the flow of groundwater and streams together, two different approaches are used, using hydraulic and hydrological models as channel flow models. The former is based on mathematical equations of water movement in open channels. In contrast, the latter is based on simplified empirical and semi-empirical relationships between the hydraulic characteristics of watercourses. In both cases, the watercourse is an internal boundary for the groundwater flow - otherwise, it is advisable to model it as a body of water. The groundwater model can be a scale model or an electrical model of the state of the groundwater or an aquifer. Groundwater models are used to represent the natural flow of groundwater in an environment. Some groundwater models include aspects of groundwater quality. Such groundwater models attempt to predict the fate and movement of a chemical in natural, urban, or hypothetical scenarios. Groundwater models can be used to predict the impact of hydrological changes on aquifer behavior and are often referred to as groundwater simulation models. Also, groundwater models are currently being used in various water management plans for urban areas. Because calculations in mathematical groundwater models are based on groundwater flow equations, which are differential equations that can often only be solved by approximate methods using numerical analysis, these models are also referred to as mathematical, numerical, or computational groundwater models.

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About one differential model of dynamics of groundwater

Abdullayev,

Hidoyatova,

Kuralov

2023

E3S Web of Conf.

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Criteria for integro-differential modeling of plane-parallel flow of viscous incompressible fluid

2023

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For a liquid with a nonmonotonic flow curve in the stationary case in the region of the descending branch, setting the velocity at the boundary does not uniquely determine the shear stress, strain rate distribution, and velocity profile that arise since the problem is known to have many unstable solutions. At the same time, the problem of the motion of such fluid under the action of a given pressure difference has no more than three solutions, two of which are stable, and the third is unstable and not reproducible. Which of the two stable solutions is realized depends on the loading history. The problem of determining the velocity profile for a fluid characterized by a nonmonotonic rheological flow curve between parallel planes is considered. The existence of a solution is realized by reducing the problem posed to a singular integral equation of normal type, which is known by the Carleman – Vekua regularization method developed by S.G. Mikhlin and M.M. Smirnov equivalently reduces to the Fredholm integral equation of the second kind, and the solvability of the latter follows from the uniqueness of the solution delivered problem describing of criteria for integro–differential modeling of a plane-parallel flow of a viscous incompressible fluid.

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In biology, solving a problem coming to a differential equation in the maple program

Nasriddinov,

Abdullayev,

Jo'rayeva

et al. 2024

E3S Web of Conf.

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We know that not only the problems of mathematics, but also the mathematical model of a number of processes that occur in nature can been reduced to a differential equation. Most of the quantities found in nature have their own laws. Finding these, laws directly have more complicated matter. Finding the relationship between the quantity in question, its rate of change and acceleration is quite easy by nature. Simple differential equations have formed as a mathematical expression of this connection. It is important and significant to use modern computer programs to find a quick and accurate solution to such equations. Found in Maple.

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A Problem with Mixed Boundary Conditions for a Singular Elliptic Equation in an Infinite Domain

Cited by 5 publications

References 13 publications

About one differential model of dynamics of groundwater

About one differential model of dynamics of groundwater

Criteria for integro-differential modeling of plane-parallel flow of viscous incompressible fluid

In biology, solving a problem coming to a differential equation in the maple program

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