scholarly journals IXED PROBLEM FOR THREE-DIMENSIONAL HYPERBOLIC EQUATIONS WITH DEGENERATION OF TYPE AND ORDER

2020 ◽  
Vol 6 (334) ◽  
pp. 13-18
Author(s):  
C. A. Aldashev ◽  
◽  
Z. N. Kanapyanova ◽  
◽  
◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Mixed Problem ◽  
Electromagnetic Fields ◽  
Hyperbolic Equations ◽  
Three Dimensional ◽  
Heat Propagation ◽  
Electromagnetic Process ◽  
Elastic Membranes ◽  
Cylindrical Region ◽  
Multidimensional Hyperbolic Equations

It is known that in space during mathematical modeling of electromagnetic fields in space, the nature of the electromagnetic process is determined by the properties of the medium. If the medium is non-conductive, then we get degenerating multidimensional hyperbolic equations. Therefore, the analysis of electromagnetic fields in complex environments (for example, if the conductivity of the medium changes) is reduced to degenerating multidimensional hyperbolic equations. It is also known that oscillations of elastic membranes in space according to the Hamilton principle can be modeled by degenerating multidimensional hyperbolic equations. Therefore, by studying mathematical modeling of the process of heat propagation in oscillating elastic membranes, we also come to degenerating multidimensional hyperbolic equations. When studying these applications, it becomes necessary to obtain a clear representation of the solutions to the investigated problems. The mixed problem for degenerating multidimensional hyperbolic equations in generalized spaces is well researched. This task is also studied in the works of S. A. Aldashev, where it is shown that its correctness significantly depends on the height of the cylindrical region under consideration. A.V. Bitsadze drew attention to the importance of studies of multidimensional hyperbolic equations with degeneration of type and order. Mixed problems for these equations have not previously been studied. In this work, the solvability of a mixed problem is shown and a clear form of a classical solution for three-dimensional hyperbolic equations with degeneration of type and order is obtained.

scholarly journals CORRECTNESS OF THE MIXED PROBLEM FOR ONE CLASS OF DEGENERATE MULTIDIMENSIONAL HYPERBOLO-PARABOLIC EQUATIONS

2020 ◽  
Vol 6 (334) ◽  
pp. 27-35
Author(s):  
C.A. Aldashev ◽  
◽  
E. Kazez ◽  
◽  
◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Mixed Problem ◽  
Electromagnetic Fields ◽  
Parabolic Equations ◽  
Hyperbolic Equations ◽  
Heat Propagation ◽  
Explicit Representation ◽  
Electromagnetic Process ◽  
Elastic Membranes ◽  
Multidimensional Hyperbolic Equations

It is known that in mathematical modeling of electromagnetic fields in space, the nature of the electromagnetic process is determined by the properties of the medium. If the medium is non-conductive, we get degenerate multi-dimensional hyperbolic equations. If the medium has a high conductivity, then we go to degenerate multidimensional parabolic equations. Consequently, the analysis of electromagnetic fields in complex media (for example, if the conductivity of the medium changes) reduces to degenerate multidimensional hyperbolic-parabolic equations. Also, it is known that the oscillations of elastic membranes in space according to the Hamilton principle can be modeled by degenerating multidimensional hyperbolic equations. Studying the process of heat propagation in a medium filled with mass leads to degenerate multidimensional parabolic equations. Consequently, by studying the mathematical modeling of the process of heat propagation in oscillating elastic membranes, we also come to degenerate multidimensional hyperbolic-parabolic equations. When studying these applications, it is necessary to obtain an explicit representation of the solutions of the studied problems. The mixed problem for degenerate multidimensional hyperbolic equations was previously considered. As far as is known, these questions for degenerate multidimensional hyperbolic-parabolic equations have not been studied. In this paper, unique solvability is shown and an explicit form of the classical solution of the mixed problem for one class of degenerate multidimensional hyperbolic-parabolic equations is obtained.

scholarly journals TRICOMI PROBLEM FOR MULTIDIMENSIONAL MIXED HYPERBOLIC-PARABOLIC EQUATION

2021 ◽  
Vol 26 (4) ◽  
pp. 7-14
Author(s):  
S. A. Aldashev
Keyword(s):  
Parabolic Equation ◽  
Electromagnetic Fields ◽  
Parabolic Equations ◽  
Hyperbolic Equations ◽  
Explicit Representation ◽  
Tricomi Problem ◽  
Electromagnetic Process ◽  
Representation Of Solutions ◽  
The Media ◽  
Multidimensional Hyperbolic Equations

It is known that in mathematical modeling of electromagnetic fields in space, the nature of the electromagnetic process is determined by the properties of the media. If the medium is non-conducting, then we obtain multidimensional hyperbolic equations. If the mediums conductivity is higher, then we arrive at multidimensional parabolic equations. Consequently, the analysis of electromagnetic fields in complex media (for example, if the conductivity of the medium changes) reduces to multidimensional hyperbolic-parabolic equations. When studying these applications, one needs to obtain an explicit representation of solutions to the problems under study. Boundary-value problems for hyperbolic-parabolic equations on a plane are well studied; however, their multidimensional analogs have been analyzed very little. The Tricomi problem for the above equations has been previously investigated, but this problem in space has not been studied earlier. This article shows that the Tricomi problem is not uniquely solvable for a multidimensional mixed hyperbolic-parabolic equation. An explicit form of these solutions is given.

scholarly journals THE WELL-POSEDNESS OF MIXED PROBLEM FOR ONE CLASS OF DEGENERATE MULTI-DIMENSIONAL HYPERBOLIC EQUATIONS

2019 ◽  
pp. 5-14
Author(s):  
S. A. Aldashev
Keyword(s):  
Boundary Value Problems ◽  
Classical Solution ◽  
Explicit Form ◽  
Mixed Problem ◽  
Unique Solvability ◽  
Hyperbolic Equations ◽  
Boundary Value ◽  
Well Posedness ◽  
Elastic Membranes ◽  
Explicit Representations

Oscillations of elastic membranes in 3D are modelled as degenerate multi-dimensional hyperbolic equations. For applied work, it is important to obtain explicit representations of solution of the studied boundary-value problems. This paper shows the unique solvability and obtains the explicit form of the classical solution of the mixed problem for degenerate multi-dimensional hyperbolic equations.

scholarly journals Radio Base Stations and Electromagnetic Fields: GIS Applications and Models for Identifying Possible Risk Factors and Areas Exposed. Some Exemplifications in Rome

2020 ◽  
Vol 10 (1) ◽  
pp. 3
Author(s):  
Cristiano Pesaresi ◽  
Davide Pavia
Keyword(s):  
Risk Factors ◽  
Electromagnetic Fields ◽  
Digital Health ◽  
Three Dimensional ◽  
Health Information System ◽  
Medical Geography ◽  
Base Stations ◽  
Buffer Zones ◽  
North East ◽  
Gis Applications

This paper—which is contextualized in the discussion on the methodological pluralism and the main topics of medical geography, the complexity theory in geographies of health, the remaking of medical geography and ad hoc systems of data elaboration—focuses on radio base stations (RBSs) as sources of electromagnetic fields, to provide GIS applications and simplifying-prudential models that are able to identify areas that could potentially be exposed to hazard. After highlighting some specific aspects regarding RBSs and their characteristics and summarizing the results of a number of studies concerning the possible effects of electromagnetic fields on health, we have taken an area of north-east Rome with a high population and building density as a case study, and we have provided some methodological and applicative exemplifications for different situations and types of antennas. Through specific functionalities and criteria, drawing inspiration from a precautionary principle, these exemplifications show some particular cases in order to support: possible risk factor identification, surveillance and spatial analysis; correlation analysis between potential risk factors and outbreak of diseases and symptoms; measurement campaigns in heavily exposed areas and buildings; education policies and prevention actions. From an operative viewpoint, we have: conducted some field surveys and recorded data and images with specific geotechnological and geomatics instruments; retraced the routes by geobrowsers and basemaps and harmonized and joined up the materials in a GIS environment; used different functions to define, on aero-satellite images, concentric circular buffer zones starting from each RBS, and geographically and geometrically delimited the connected areas subject to high and different exposure levels; produced digital applications and tested prime three-dimensional models, in addition to a video from a bird’s eye view perspective, able to show the buildings in the different buffer zones and which are subject to a hazard hierarchy due to exposure to an RBS. A similar GIS-based model—reproposable with methodological adjustments to other polluting sources—can make it possible to conceive a dynamic and multiscale digital system functional in terms of strategic planning, decision-making and public health promotion in a performant digital health information system.

Sign in / Sign up

Export Citation Format

Share Document