On Solvability of a Poincare–Tricomi Type Problem for an Elliptic–Hyperbolic Equation of the Second Kind

Yuldashev, T. K.; Islomov, B. I.; Abdullaev, A. A.

doi:10.1134/s1995080221030239

Cited by 31 publications

(4 citation statements)

References 18 publications

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“…The difference of the value from zero gives reason to believe that there is a significant autocorrelation between the yield of cotton. Consequently, the yield of cotton in the Bukhara region this year depends on the yield of past years 𝑅 𝐿 [8][9][10][11][12][13][14][15]. Based on sample data, using the x7.2019 program package and Excel computer, the numerical characteristics of the average cotton yield -𝑦 𝑡 in the Bukhara region are calculated (Table 4):…”

Section: Discussionmentioning

confidence: 99%

Statistical analysis and forecasting of cotton yield dynamics in Bukhara region

Vakhabov,

Fayziev

2023

E3S Web of Conf.

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Observations on some phenomena, the nature of which changes in time, are ordered sequences, which is called the time series. In the article, by the method of statistical analysis of time series, the statistical regularity of the series of dynamics of the average yield of cotton in the Bukhara region, the Republic of Uzbekistan (based on the materials of the CSO of the Republic of Uzbekistan for 2001-2019) was studied. Point and interval estimates for the average cotton yield were built with a 95% guarantee, explicit types of trends were determined, and yields in the region were predicted for subsequent years. With the help of Durbin-Watson statistical criteria, it was found that the average cotton yield in the region has an autocorrelation dependence.

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Section: Discussionmentioning

confidence: 99%

Statistical analysis and forecasting of cotton yield dynamics in Bukhara region

Vakhabov,

Fayziev

2023

E3S Web of Conf.

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“…But on the other hand, by virtue of the Zaremba-Giraud principle [24], [26], for the solution of equation ( 1), taking into account (15), we have…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…Therefore, the study of non-local boundary value problems with a conormal derivative for equations of mixed elliptic-hyperbolic type of the second kindseems to be very relevant and little studied. Note the works [14,15]. In this paper, we study a nonlocal boundary value problem with the Poincaré condition for an elliptichyperbolic type equation of the second kind, i.e.…”

Section: Introductionmentioning

confidence: 99%

On the unique solvability of a nonlocal boundary value problem with the poincaré condition

2023

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As is known, it is customary in the literature to divide degenerate equations of mixed type into equations of the first and second kind. In the case of an equation of the second kind, in contrast to the first, the degeneracy line is simultaneously the envelope of a family of characteristics, i.e. is itself a characteristic, which causes additional difficulties in the study of boundary value problems for equations of the second kind. In this paper, in order to establish the unique solvability of one nonlocal problem with the Poincaré condition for an elliptic-hyperbolic equation of the second kind developed a new principle extremum, which helps to prove the uniqueness of resolutions as signed problem. The existence of a solution is realized by reducing the problem posed to a singular integral equation of normal type, which 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.

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“…z x y is the generalized solution of the Cauchy problem for the equation 0 2 z L in the domain of from the class ܴ ଶ then has representation(7…”

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confidence: 99%

About one boundary-value problem arising in modeling dynamics of groundwater

2023

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Modeling the movement of moisture in the soil is of great importance for assessing the impact of agricultural land on surface water bodies and, consequently, on the natural environment and humans. This is because huge volumes of pollutants from the fields (pesticides, mineral fertilizers, nitrates, and nutrients contained in them) are transferred to reservoirs by filtering moisture. Different methods solve all these tasks. The method of natural analogies is based on the analysis of graphs of fluctuations in groundwater level. To apply this method on irrigated lands, it is necessary to have a sufficiently studied irrigated area with similar natural, organizational and economic conditions. The successful application of this method, based on the fundamental theory of physical similarity, mainly depends on the availability of a sufficiently close comparison object, which is quite rare in practice. Physical modeling is often used to construct dams and other hydraulic structures. Previously, the method of electrical modeling was also widely used. It was further found that nonlocal boundary conditions arise in the problems of predicting soil moisture, modeling fluid filtration in porous media, mathematical modeling of laser radiation processes, and plasma physics problems, as well as mathematical biology.

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On Solvability of a Poincare–Tricomi Type Problem for an Elliptic–Hyperbolic Equation of the Second Kind

Cited by 31 publications

References 18 publications

Statistical analysis and forecasting of cotton yield dynamics in Bukhara region

Statistical analysis and forecasting of cotton yield dynamics in Bukhara region

On the unique solvability of a nonlocal boundary value problem with the poincaré condition

About one boundary-value problem arising in modeling dynamics of groundwater

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