On linear differential equations with transformed argument solvable by means of right invertible operators

Przeworska-Rolewicz, Danuta

doi:10.4064/ap-29-2-141-148

Cited by 8 publications

(7 citation statements)

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“…Equations with involutions have been studied by many researchers, for example, Ashyralyev [5,6], Babbage [7], Przewoerska-Rolewicz [27,28,29,30,31,32,33], Aftabizadeh and Col. [1], Andreev [3,4], Burlutskayaa and Col. [8], Gupta [13,14,15], Kirane [19], Watkins [39], and Wiener [40,41,42,43]. Spectral problems and inverse problems for equations with involutions have received a lot of attention as well, see for example, [18,22,35,36,37], and equations with a delay in the space variable have been the subject of many research papers, see for example, [2,34].…”

Section: Introductionmentioning

confidence: 99%

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On a class of inverse problems for a heat equation with involution perturbation

Al-Salti¹,

Kirane²,

Torebek

2017

HJMS

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A class of inverse problems for a heat equation with involution perturbation is considered using four different boundary conditions, namely, Dirichlet, Neumann, periodic and anti-periodic boundary conditions. Proved theorems on existence and uniqueness of solutions to these problems are presented. Solutions are obtained in the form of series expansion using a set of appropriate orthogonal basis for each problem. Convergence of the obtained solutions is also discussed.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On a class of inverse problems for a heat equation with involution perturbation

Al-Salti¹,

Kirane²,

Torebek

2017

HJMS

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“…This class of problem has extensive applications in engineering 11,12 . For more details about the theoretic development and the physical motivation of these equations, the reader is referred to previous studies 10,13‐22 and the monographs 1,2 …”

Section: Position Of the Problemmentioning

confidence: 99%

A variant of quasi‐reversibility method for a class of heat equations with involution perturbation

Roumaissa

Boussetila

Rebbani³

2020

Math Methods in App Sciences

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The paper is devoted to investigating a Cauchy problem governed by nonclassical heat equation with involution. The problem is severely ill‐posed in the sense of Hadamard by violating the continuous dependence upon the input Cauchy data. Therefore, in order to obtain a stable solution, we shall use a modified Pseudo‐Parabolic Regularization Method. The main idea is to add a correction term by introducing a third‐order derivation operator to formulate a sequence of well‐posed problems that depend on a regularization parameter ε. Further, we show that the approximate problems are well posed, and we prove some convergence results.

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“…Here α(t) is a changing orientation homeomorphism α(t) : [0, T ] → [0, T ] such that α 2 (t) = α (α(t)) = t. Such a homeomorphism is called a Carleman shift or deviation of involution. Its properties were studied by G. Litvinchuk [1], N. Karapetyants and S. Samko [2] and other (see [3], [4], [5], [6], [7], [8], [9], [10]). As an example of a deviation with involution on [0, T ] we can take the homeomorphism α(t) = T − t.…”

Section: Introductionmentioning

confidence: 99%