On the spectrum of Volterra integral equation with the “incompressible” kernel

Amangaliyeva, Meiramkul; Jenaliyev, Muvasharkhan; Kosmakova, M.T.; Ramazanov, M.I.

doi:10.1063/1.4893816

Cited by 8 publications

(13 citation statements)

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“…In this connection, the weight classes of the solution existence differ from the class of the solution existence for the equation considered in this work. We also note that boundary value problems for a spectrally loaded parabolic equation reduce to this kind of singular integral equations, when the load line moves according to the law x = t [5-10] and problems for essentially loaded equation of heat conduction [11][12][13][14][15].…”

Section: Resultsmentioning

confidence: 99%

On the integral equation of an adjoint boundary value problem of heat conduction

Kosmakova¹,

Romanovski²,

Orumbayeva³

et al. 2019

Bul. Kar. Univ. - Math.

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An integral equation is considered, to which a nonhomogeneous first boundary value problem with an adjoint heat conduction operator is reduced. The problem is set in an infinite plane angle, that is, a boundary of the domain moves with a constant velocity, and the domain degenerates to a point at the initial moment of time. The incompressibility of the integral operator for the equation under study is shown. Using the relations for an independent variable, the equation under study is equivalently reduced to a certain simplified equation. With the help of replacements for independent variables, the equation is reduced to an integral equation with a difference kernel. By applying the Laplace transform, the obtained equation is reduced to an ordinary first-order differential equation (linear). Its solution is found. By using the inverse Laplace transform, a solution of the nonhomogeneous integral equation under study is obtained in the form of a convergent series in some domain.

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Section: Resultsmentioning

confidence: 99%

On the integral equation of an adjoint boundary value problem of heat conduction

Kosmakova¹,

Romanovski²,

Orumbayeva³

et al. 2019

Bul. Kar. Univ. - Math.

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“…It will be shown that the characteristics that were inherent to that considered in [18][19][20] are maintained. This is the mathematical explanation of special effects in the very beginning moment of time of contacts breaking or in the final moment of time of contacts closure.…”

Section: Numerical Example the Optimal Motion Control Of Two-unit Elmentioning

confidence: 99%

“…The results of the problem (34)-(35) are described in detail and published in papers [18][19][20]. Here we first briefly present the results of these works, and then consider their application to other tasks, the relevant cases: (a) one contact is stationary and the other moves with an arbitrary constant given speed, not necessarily equal to one; (b) both contacts move at the same velocity in the process of breaking.…”

Section: Numerical Example the Optimal Motion Control Of Two-unit Elmentioning

confidence: 99%

“…In this paper, we applied the results of papers [18][19][20][21] for the cases when either only one part of the contact moves with an arbitrary constant, but not necessarily with unit speed or both contact parts are moving with respective constant speeds. The investigation showed that a significant feature of the thermal conditions in the contact space appears at moments of either contact closing or opening, which is of the order ≈ t −1/2 .…”

Section: About Modeling Of Thermal Processes In Electric Contact Devicesmentioning

confidence: 99%

“…Previously we determined the results (see Clause 8) for the case of closed or open contact on condition that one part of the contact does not move and the other part of the contact moves with the single constant speed [18][19][20][21].…”

Section: About Modeling Of Thermal Processes In Electric Contact Devicesmentioning

confidence: 99%

See 2 more Smart Citations

To the theory of modeling of electric power and electric contact systems

Kalimoldayev

Jenaliyev

2016

Open Engineering

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This study evaluated questions of optimum control solution of ordinary differential equations' nonlinear system which in particular, describes control processes of electric power systems. Conducted numerical experiments have shown sufficient efficiency of the implemented algorithms. It has been shown that essential feature of heating conditions in contact space occur in the moment of contact closure or contact breaking, which has t −1/2 order.

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On a pseudo-Volterra nonhomogeneous integral equation

Kosmakova¹,

Akhmanova²,

Tuleutaeva³

et al. 2019

Bul. Kar. Univ. - Math.

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In this paper the issues of the solvability of a pseudo-Volterra nonhomogeneous integral equation of the second kind are studied. The solution to the corresponding homogeneous equation and the classes of the uniqueness of the solution are found in [1]. By replacing the right-hand side and the unknown function, the integral equation is reduced to an integral equation, the kernel of which is not compressible. Using the Laplace transform, the obtained equation is reduced to an ordinary first-order differential equation (linear). Its solution is found. By using the solution of the homogeneous equation the form of a particular solution of the nonhomogeneous differential equation is defined (by the variation method of an arbitrary constant). By using the inverse Laplace transform, a particular solution of the pseudo-Volterra nonhomogeneous integral equation under study is obtained. The case of an nonhomogeneous integral equation with the value of the parameter k = 1 is considered and studied. Classes for the right side and the solution of the integral equation are indicated.

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On the spectrum of Volterra integral equation with the “incompressible” kernel

Cited by 8 publications

References 0 publications

On the integral equation of an adjoint boundary value problem of heat conduction

On the integral equation of an adjoint boundary value problem of heat conduction

To the theory of modeling of electric power and electric contact systems

On a pseudo-Volterra nonhomogeneous integral equation

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