Existence and uniqueness of solutions for nonlinear impulsive differential equations with two-point and integral boundary conditions

Ashyralyev, Allaberen; Sharifov, Yagub A.

doi:10.1186/1687-1847-2013-173

Cited by 34 publications

(14 citation statements)

References 11 publications

(1 reference statement)

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“…, k ∈ N, and the constants C k,i and f k,i are unknown. To find these constants, we use conditions (14) and (15). From (14), we obtain a unique solution of the Cauchy problem (13) and (14) in the form…”

Section: Uniqueness Of the Solution Of The Problemmentioning

confidence: 99%

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On an inverse problem of reconstructing a subdiffusion process from nonlocal data

Kirane

Sadybekov

Sarsenbi

2019

Math Methods in App Sciences

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We consider a problem of modeling the thermal diffusion process in a closed metal wire wrapped around a thin sheet of insulation material. The layer of insulation is assumed to be slightly permeable. Therefore, the temperature value from one side affects the diffusion process on the other side. For this reason, the standard heat equation is modified, and a third term with an involution is added. Modeling of this process leads to the consideration of an inverse problem for a one‐dimensional fractional evolution equation with involution and with periodic boundary conditions with respect to a space variable. This equation interpolates heat equation. Such equations are also called nonlocal subdiffusion equations or nonlocal heat equations. The inverse problem consists in the restoration (simultaneously with the solution) of the unknown right‐hand side of the equation, which depends only on the spatial variable. The conditions for overdefinition are initial and final states. Existence and uniqueness results for the given problem are obtained via the method of separation of variables.

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Section: Uniqueness Of the Solution Of The Problemmentioning

confidence: 99%

“…Substituting (21) and (22) into Equation 5, we obtain the inverse problems (13) to (15). If the constants k,i are assumed to be given, then the solutions of these inverse problems exist, are unique, and are represented by formulas (16) and (19).…”

Section: Construction Of a Formal Solution Of The Problemmentioning

confidence: 99%

On an inverse problem of reconstructing a subdiffusion process from nonlocal data

Kirane

Sadybekov

Sarsenbi

2019

Math Methods in App Sciences

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“…Let us cite papers only those of them that are most close to the subject under consideration [12][13][14][15][16].…”

Section: The Mathematical Problemmentioning

confidence: 99%

An inverse problem of mathematical modeling of the extraction process of polydisperse porous materials

Orazov¹,

Makhatova²

2014

AIP Conference Proceedings

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In this paper, we consider one family of problems simulating the determination of target components and density of sources from given values of the initial and final states. The mathematical statement of these problems leads to the inverse problem for the diffusion equation, where it is required to find not only a solution of the problem, but also its right-hand side that depends only on a spatial variable. A specific feature of the considered problems is that the system of eigenfunctions of the multiple differentiation operator subject to boundary conditions of the initial problem does not have the basis property. We prove the unique existence of a generalized solution of the problem.

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“…Some authors have produced an extensive portfolio of results on differential equations undergoing impulse effects. The existence questions for impulsive differential equations have been studied in [10][11][12][13][14][15][16][17][18][19] and references therein. Three-point boundary value problems for ordinary differential equations are also studied in recent years.…”

Section: Introductionmentioning

confidence: 99%

Existence and uniqueness of solutions for nonlinear impulsive differential equations with three-point boundary conditions

Mardanov

Sharifov

Ismayilova

2018

E-Journal of Analysis and Applied Mathematics

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This paper is devoted to a system of nonlinear impulsive differential equations with three-point boundary conditions. The Green function is constructed and considered original problem is reduced to the equivalent impulsive integral equations. Sufficient conditions are found for the existence and uniqueness of solutions for the boundary value problems for the first order nonlinear system of the impulsive ordinary differential equations with three-point boundary conditions. The Banach fixed point theorem is used to prove the existence and uniqueness of a solution of the problem and Schaefer's fixed point theorem is used to prove the existence of a solution of the problem under consideration. We illustrate the application of the main results by two examples.

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Existence and uniqueness of solutions for nonlinear impulsive differential equations with two-point and integral boundary conditions

Cited by 34 publications

References 11 publications

On an inverse problem of reconstructing a subdiffusion process from nonlocal data

On an inverse problem of reconstructing a subdiffusion process from nonlocal data

An inverse problem of mathematical modeling of the extraction process of polydisperse porous materials

Existence and uniqueness of solutions for nonlinear impulsive differential equations with three-point boundary conditions

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