Boundary value problems for a weakly loaded operator of a second-order hyperbolic equation in a cylindrical domain
By using methods of functional analysis, we prove the existence and uniqueness, in appropriate function spaces, of solutions of boundary value problems for a second-order linear hyperbolic equation weakly loaded by a differential operator. The order of the operator in the loaded term with respect to...
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| Published in: | Differential equations Vol. 51; no. 12; pp. 1595 - 1606 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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Moscow
Pleiades Publishing
01-12-2015
Springer Nature B.V |
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| Abstract | By using methods of functional analysis, we prove the existence and uniqueness, in appropriate function spaces, of solutions of boundary value problems for a second-order linear hyperbolic equation weakly loaded by a differential operator. The order of the operator in the loaded term with respect to its derivatives is equal to 2. |
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| AbstractList | By using methods of functional analysis, we prove the existence and uniqueness, in appropriate function spaces, of solutions of boundary value problems for a second-order linear hyperbolic equation weakly loaded by a differential operator. The order of the operator in the loaded term with respect to its derivatives is equal to 2. |
| Author | Kozlovskaya, I. S. Dzhenaliev, M. T. Korzyuk, V. I. |
| Author_xml | – sequence: 1 givenname: V. I. surname: Korzyuk fullname: Korzyuk, V. I. email: korzyuk@bsu.by organization: Belarusian State University, Institute of Mathematics and Mathematical Modeling – sequence: 2 givenname: M. T. surname: Dzhenaliev fullname: Dzhenaliev, M. T. organization: Belarusian State University, Institute of Mathematics and Mathematical Modeling – sequence: 3 givenname: I. S. surname: Kozlovskaya fullname: Kozlovskaya, I. S. organization: Belarusian State University, Institute of Mathematics and Mathematical Modeling |
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| Cites_doi | 10.5802/aif.55 10.1007/978-3-663-11374-4 10.4213/mzm156 |
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| DOI | 10.1134/S0012266115120071 |
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| References | Dzhenaliev, Ramazanov (CR7) 2007; 43 Korzyuk (CR10) 2013 Burenkov (CR13) 1987; 180 Deny, Lions (CR11) 1953; 5 Dzhenaliev (CR3) 1995 Nakhushev (CR2) 1995 Dzhenaliev (CR4) 2001; 37 Nakhushev (CR1) 1983; 19 Dzhenaliev, Ramazanov (CR6) 2007 Kozhanov (CR5) 2004; 76 Dzhenaliev, Ramazanov (CR9) 2006; 47 Dzhenaliev, Ramazanov (CR8) 2007; 43 Burenkov (CR12) 1998 M.T. Dzhenaliev (260_CR7) 2007; 43 A.M. Nakhushev (260_CR1) 1983; 19 M.T. Dzhenaliev (260_CR4) 2001; 37 M.T. Dzhenaliev (260_CR6) 2007 M.T. Dzhenaliev (260_CR8) 2007; 43 A.I. Kozhanov (260_CR5) 2004; 76 J. Deny (260_CR11) 1953; 5 M.T. Dzhenaliev (260_CR3) 1995 M.T. Dzhenaliev (260_CR9) 2006; 47 A.M. Nakhushev (260_CR2) 1995 V.I. Korzyuk (260_CR10) 2013 V.I. Burenkov (260_CR12) 1998 V.I. Burenkov (260_CR13) 1987; 180 |
| References_xml | – volume: 43 start-page: 498 issue: 4 year: 2007 end-page: 508 ident: CR7 article-title: On a Boundary Value Problem for a Spectrally Loaded Heat Operator. I publication-title: Differ. Uravn. contributor: fullname: Ramazanov – start-page: 114 year: 2007 end-page: 127 ident: CR6 article-title: Boundary Value Problems for Spectrally Loaded Parabolic Operators publication-title: Neklassicheskie uravneniya matematicheskoi fiziki contributor: fullname: Ramazanov – volume: 37 start-page: 48 issue: 1 year: 2001 end-page: 54 ident: CR4 article-title: On Loaded Equations with Periodic Boundary Conditions publication-title: Differ. Uravn. contributor: fullname: Dzhenaliev – volume: 5 start-page: 305 year: 1953 end-page: 370 ident: CR11 article-title: Les espaces du type de Beppo Levi publication-title: Ann. Inst. Fourier doi: 10.5802/aif.55 contributor: fullname: Lions – year: 1998 ident: CR12 publication-title: Sobolev Spaces on Domains doi: 10.1007/978-3-663-11374-4 contributor: fullname: Burenkov – volume: 76 start-page: 84 issue: 6 year: 2004 end-page: 91 ident: CR5 article-title: On a Certain Nonlinear Loaded Parabolic Equation and a Related Inverse Problem publication-title: Mat. Zametki doi: 10.4213/mzm156 contributor: fullname: Kozhanov – volume: 180 start-page: 68 year: 1987 end-page: 70 ident: CR13 article-title: Approximation by Infinitely Differentiable Functions with Preservation of Boundary Values publication-title: Tr. Mat. Inst. Akad. Nauk SSSR contributor: fullname: Burenkov – volume: 47 start-page: 527 issue: 3 year: 2006 end-page: 547 ident: CR9 article-title: On a Boundary Value Problem for a Spectrally Loaded Heat Operator publication-title: Sibirsk. Mat. Zh. contributor: fullname: Ramazanov – year: 1995 ident: CR3 publication-title: K teorii lineinykh kraevykh zadach dlya nagruzhennykh differentsial’nykh uravnenii contributor: fullname: Dzhenaliev – volume: 43 start-page: 788 issue: 6 year: 2007 end-page: 794 ident: CR8 article-title: On a Boundary Value Problem for a Spectrally Loaded Heat Operator. II publication-title: Differ. Uravn. contributor: fullname: Ramazanov – year: 1995 ident: CR2 publication-title: Uravneniya matematicheskoi biologii contributor: fullname: Nakhushev – volume: 19 start-page: 86 issue: 1 year: 1983 end-page: 94 ident: CR1 article-title: Loaded Equations and Their Applications publication-title: Differ. Uravn. contributor: fullname: Nakhushev – year: 2013 ident: CR10 publication-title: Metod energeticheskikh neravenstv i operatorov osredneniya. Granichnye zadachi dlya differentsial’nykh uravnenii s chastnymi proizvodnymi contributor: fullname: Korzyuk – volume-title: Uravneniya matematicheskoi biologii year: 1995 ident: 260_CR2 contributor: fullname: A.M. Nakhushev – volume: 47 start-page: 527 issue: 3 year: 2006 ident: 260_CR9 publication-title: Sibirsk. Mat. Zh. contributor: fullname: M.T. Dzhenaliev – volume: 43 start-page: 498 issue: 4 year: 2007 ident: 260_CR7 publication-title: Differ. Uravn. contributor: fullname: M.T. Dzhenaliev – volume: 5 start-page: 305 year: 1953 ident: 260_CR11 publication-title: Ann. Inst. Fourier doi: 10.5802/aif.55 contributor: fullname: J. Deny – start-page: 114 volume-title: Neklassicheskie uravneniya matematicheskoi fiziki year: 2007 ident: 260_CR6 contributor: fullname: M.T. Dzhenaliev – volume-title: Metod energeticheskikh neravenstv i operatorov osredneniya. Granichnye zadachi dlya differentsial’nykh uravnenii s chastnymi proizvodnymi year: 2013 ident: 260_CR10 contributor: fullname: V.I. Korzyuk – volume: 180 start-page: 68 year: 1987 ident: 260_CR13 publication-title: Tr. Mat. Inst. Akad. Nauk SSSR contributor: fullname: V.I. Burenkov – volume: 19 start-page: 86 issue: 1 year: 1983 ident: 260_CR1 publication-title: Differ. Uravn. contributor: fullname: A.M. Nakhushev – volume-title: K teorii lineinykh kraevykh zadach dlya nagruzhennykh differentsial’nykh uravnenii year: 1995 ident: 260_CR3 contributor: fullname: M.T. Dzhenaliev – volume: 76 start-page: 84 issue: 6 year: 2004 ident: 260_CR5 publication-title: Mat. Zametki doi: 10.4213/mzm156 contributor: fullname: A.I. Kozhanov – volume-title: Sobolev Spaces on Domains year: 1998 ident: 260_CR12 doi: 10.1007/978-3-663-11374-4 contributor: fullname: V.I. Burenkov – volume: 37 start-page: 48 issue: 1 year: 2001 ident: 260_CR4 publication-title: Differ. Uravn. contributor: fullname: M.T. Dzhenaliev – volume: 43 start-page: 788 issue: 6 year: 2007 ident: 260_CR8 publication-title: Differ. Uravn. contributor: fullname: M.T. Dzhenaliev |
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| SubjectTerms | Applied mathematics Boundary conditions Boundary value problems Derivatives Difference and Functional Equations Differential equations Euclidean space Function space Functional analysis Mathematical analysis Mathematical functions Mathematical models Mathematics Mathematics and Statistics Operators (mathematics) Ordinary Differential Equations Partial Differential Equations Studies Uniqueness |
| Title | Boundary value problems for a weakly loaded operator of a second-order hyperbolic equation in a cylindrical domain |
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