Boundary-Value Problems for Loaded Third-Order Parabolic-Hyperbolic Equations in Infinite Three-Dimensional Domains

Yuldashev, T. K.; Islomov, B. I.; Alikulov, E. K.

doi:10.1134/s1995080220050145

Cited by 41 publications

(8 citation statements)

References 14 publications

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“…This proves the uniqueness of the solution of the problem AG * 1λ for the equation (14). Further, taking into account (40) and (41), from (13) we have (42) u (x, y, λ) ≡ 0, (x, y) ∈ D.…”

Section: Investigation Of the Agsupporting

confidence: 55%

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Analogues of the Cauchy–Goursat problem for a loaded third-order hyperbolic type equation in an infinite three-dimensional domain

Islomov¹,

Alikulov²

2021

Sib. Elektron. Mat. Izv.

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In this article it is studied the analogue of CauchyGoursat problem for a loaded third-order hyperbolic type dierential equation in an innite three-dimensional domain. The main research method is the Fourier transform of studying the analogous of the CauchyGoursat problem. Based on this Fourier transform, the given problem reduces to a at analogue of the CauchyGoursat problem with a spectral parameter with boundary value conditions. The asymptotic behavior of the solution of plane analogues of the CauchyGoursat problem for large values of the spectral parameter is studied. Sucient conditions are obtained, according to which all operations in this paper are legal.

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Section: Investigation Of the Agsupporting

confidence: 55%

“…We note, that the boundary value problems for the loaded third-order dierential equations of hyperbolic, mixed and mixed-composite types in innite threedimensional domain studied a little (here we refer the readers to the works [42,43]).…”

Section: Introductionmentioning

confidence: 99%

Analogues of the Cauchy–Goursat problem for a loaded third-order hyperbolic type equation in an infinite three-dimensional domain

Islomov¹,

Alikulov²

2021

Sib. Elektron. Mat. Izv.

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“…When modelling the problems of optimal control of the agroeconomic system for regulating groundwater marks and soil moisture, it became necessary to study boundary value problems for loaded partial differential equations [27,28]. A large number of publications, in particular, [29][30][31][32][33], have been devoted to study of boundary value problems of various kinds for loaded equations of parabolic, parabolichyperbolic and elliptic-hyperbolic and other types.…”

Section: Introductionmentioning

confidence: 99%

Unique Solvability of a Boundary Value Problem for a Loaded Fractional Parabolic-Hyperbolic Equation with Nonlinear Terms

Yuldashev

Абдуллаев

2021

Lobachevskii J Math

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This work is devoted to study the existence and uniqueness of solution of an analogue of the Gellerstedt problem with nonlocal assumptions on the boundary and integral gluing conditions for the parabolic-hyperbolic type equation with nonlinear terms and Gerasimov–Caputo operator of differentiation. Using the method of integral energy, the uniqueness of solution have been proved. Existence of solution was proved by the method of successive approximations of factorial law for Volterra type nonlinear integral equations.

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“…Boundary value problems for a second-order mixed parabolic-hyperbolic equation in a three-dimensional prismatic domain were studied in [18]. We note, that the boundary value problems for the loaded third-order differential equations of hyperbolic, mixed and mixed-composite types in infinite three-dimensional domain were few studied (in [19], [20]).…”

Section: Introductionmentioning

confidence: 99%

Boundary Value Problem for Loaded Equation of Parabolic-Hyperbolic Type of the Third Order in an Infinite Three-Dimensional Domain

Islomov¹,

Alikulov²

2021

Int. J. of Appl. Math.

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Boundary-Value Problems for Loaded Third-Order Parabolic-Hyperbolic Equations in Infinite Three-Dimensional Domains

Cited by 41 publications

References 14 publications

Analogues of the Cauchy–Goursat problem for a loaded third-order hyperbolic type equation in an infinite three-dimensional domain

Analogues of the Cauchy–Goursat problem for a loaded third-order hyperbolic type equation in an infinite three-dimensional domain

Unique Solvability of a Boundary Value Problem for a Loaded Fractional Parabolic-Hyperbolic Equation with Nonlinear Terms

Boundary Value Problem for Loaded Equation of Parabolic-Hyperbolic Type of the Third Order in an Infinite Three-Dimensional Domain

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