Boundary-Value Problem for a Degenerate High-Odd-Order Equation

Apakov, Yu. P.; Irgashev, B. Yu.

doi:10.1007/s11253-015-1039-7

Cited by 22 publications

(3 citation statements)

References 2 publications

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“…Rustamova in [11]. Many authors also studied boundary value problems for degenerate equations [12][13][14]. In the present paper, the boundary value problem is studied for the fourth-order degenerate equation in a rectangular domain.…”

Section: Introductionmentioning

confidence: 99%

A boundary value problem for the fourth-order degenerate equation of the mixed type

Otarova

2024

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Many problems in mechanics, physics, and geophysics lead to solving partial differential equations that are not included in the known classes of elliptic, parabolic or hyperbolic equations. Such equations, as a rule, began to be called non-classical equations of mathematical physics. The theory of degenerate equations is one of the central branches of the modern theory of partial differential equations. This is primarily due to the identification of a variety of applied problems, the mathematical modeling of which serves the study of various types of degenerate equations. The study of boundary value problems for mixed type’s equations of the fourth-order with power-law degeneration remains relevant. In this work, a boundary value problem in a rectangular domain for a degenerate equation of the fourth-order mixed-type is posed and investigated. Well-posedness of the boundary value problem for a fourth-order partial differential equation is established by proving the existence and uniqueness of the solution. Under sufficient conditions, a solution to the problem under consideration was explicitly found by the variable separation method.

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Section: Introductionmentioning

confidence: 99%

A boundary value problem for the fourth-order degenerate equation of the mixed type

Otarova

2024

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“…The monograph [5] is devoted to the classification of fourthorder partial differential equations and the solution of boundary-value problems for these equations. A series of well-posed boundary-value problems for third-order equations with multiple characteristics was studied in [6][7][8][9][10][11]. A problem for an inhomogeneous equation of the fourth order with a single minor term was considered in [12].…”

Section: Introductionmentioning

confidence: 99%

Boundary-Value Problem for the Fourth-Order Equation with Multiple Characteristics in a Rectangular Domain

Apakov

Mamajonov

2023

J Math Sci

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“…Such problems have formed various research fields. Several nonlocal and local boundary value problems for differential equations have been investigated extensively in various works (for example, see [4][5][6][7][8][9][10][11][12] and the references given therein).…”

Section: Introductionmentioning

confidence: 99%

On the Absolute Stable Difference Scheme for Third Order Delay Partial Differential Equations

2020

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The initial value problem for the third order delay differential equation in a Hilbert space with an unbounded operator is investigated. The absolute stable three-step difference scheme of a first order of accuracy is constructed and analyzed. This difference scheme is built on the Taylor’s decomposition method on three and two points. The theorem on the stability of the presented difference scheme is proven. In practice, stability estimates for the solutions of three-step difference schemes for different types of delay partial differential equations are obtained. Finally, in order to ensure the coincidence between experimental and theoretical results and to clarify how efficient the proposed scheme is, some numerical experiments are tested.

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Boundary-Value Problem for a Degenerate High-Odd-Order Equation

Cited by 22 publications

References 2 publications

A boundary value problem for the fourth-order degenerate equation of the mixed type

A boundary value problem for the fourth-order degenerate equation of the mixed type

Boundary-Value Problem for the Fourth-Order Equation with Multiple Characteristics in a Rectangular Domain

On the Absolute Stable Difference Scheme for Third Order Delay Partial Differential Equations

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