Boundary-Value Problem for Systems of Convolutional Equations in Anisotropic Functional Spaces
In this paper, anisotropic classes of well-posed Cauchy problems and boundary-value problems for systems of convolutions equations are obtained. For a particular case of differential equations, a hypersurface of conjugate orders of the corresponding polynomial is used, and various classes of well-po...
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| Published in | Journal of mathematical sciences (New York, N.Y.) Vol. 277; no. 5; pp. 770 - 773 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Cham
Springer International Publishing
22.12.2023
Springer Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1072-3374 1573-8795 |
| DOI | 10.1007/s10958-023-06886-0 |
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| Abstract | In this paper, anisotropic classes of well-posed Cauchy problems and boundary-value problems for systems of convolutions equations are obtained. For a particular case of differential equations, a hypersurface of conjugate orders of the corresponding polynomial is used, and various classes of well-posed problems are obtained. |
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| AbstractList | In this paper, anisotropic classes of well-posed Cauchy problems and boundary-value problems for systems of convolutions equations are obtained. For a particular case of differential equations, a hypersurface of conjugate orders of the corresponding polynomial is used, and various classes of well-posed problems are obtained. Keywords and phrases: convolution equation, boundary-value problem, Fourier transform, hypersurface of conjugate orders, anisotropic space of functions. AMS Subject Classification: 35A05, 35S10 In this paper, anisotropic classes of well-posed Cauchy problems and boundary-value problems for systems of convolutions equations are obtained. For a particular case of differential equations, a hypersurface of conjugate orders of the corresponding polynomial is used, and various classes of well-posed problems are obtained. |
| Audience | Academic |
| Author | Makarov, A. A. |
| Author_xml | – sequence: 1 givenname: A. A. surname: Makarov fullname: Makarov, A. A. email: natvasmak@ukr.net organization: Kharkov National University |
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| Cites_doi | 10.1070/RM1972v027n04ABEH003368 |
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| Copyright | Springer Nature Switzerland AG 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. COPYRIGHT 2023 Springer |
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| Keywords | 35A05 35S10 Fourier transform anisotropic space of functions boundary-value problem convolution equation hypersurface of conjugate orders |
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| References | L. R. Volevich and S. G. Gindikin, “Cauchy problem and related problems for convolution-type equations,” Usp. Mat. Nauk, 27, No. 4 (166), 65–143 (1972). G. P. Serdyuk, On the uniqueness of solutions of linear differential equations [in Russian], Ph.D. Thesis, Kharkov (1983). VolevichLRGindikinSGGeneralized Functions and Convolution Equations1994MoscowFizmatlit[in Russian] A. A. Makarov, “Solvability criterion for boundary-value problems in a layer for a system of linear convolution equations in topological spaces,” in: Theoretical and Applied Problems of Differential Equations and Algebra, Naukova Dumka, Kiev (1978), pp. 178–180. MakarovAAOn necessary and sufficient solvability conditions for boundary-value problems in a layer for a system of partial differential equationsDiffer. Uravn.1981172320324 6886_CR1 6886_CR3 LR Volevich (6886_CR2) 1994 AA Makarov (6886_CR4) 1981; 17 6886_CR5 |
| References_xml | – reference: L. R. Volevich and S. G. Gindikin, “Cauchy problem and related problems for convolution-type equations,” Usp. Mat. Nauk, 27, No. 4 (166), 65–143 (1972). – reference: MakarovAAOn necessary and sufficient solvability conditions for boundary-value problems in a layer for a system of partial differential equationsDiffer. Uravn.1981172320324 – reference: VolevichLRGindikinSGGeneralized Functions and Convolution Equations1994MoscowFizmatlit[in Russian] – reference: G. P. Serdyuk, On the uniqueness of solutions of linear differential equations [in Russian], Ph.D. Thesis, Kharkov (1983). – reference: A. A. Makarov, “Solvability criterion for boundary-value problems in a layer for a system of linear convolution equations in topological spaces,” in: Theoretical and Applied Problems of Differential Equations and Algebra, Naukova Dumka, Kiev (1978), pp. 178–180. – ident: 6886_CR3 – ident: 6886_CR1 doi: 10.1070/RM1972v027n04ABEH003368 – volume-title: Generalized Functions and Convolution Equations year: 1994 ident: 6886_CR2 – volume: 17 start-page: 320 issue: 2 year: 1981 ident: 6886_CR4 publication-title: Differ. Uravn. – ident: 6886_CR5 |
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| Snippet | In this paper, anisotropic classes of well-posed Cauchy problems and boundary-value problems for systems of convolutions equations are obtained. For a... |
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| SubjectTerms | Anisotropy Boundary value problems Cauchy problems Differential equations Hyperspaces Mathematical analysis Mathematics Mathematics and Statistics Polynomials Well posed problems |
| Title | Boundary-Value Problem for Systems of Convolutional Equations in Anisotropic Functional Spaces |
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