An efficient abstract method for the study of an initial boundary value problem on singular domain
The present work is devoted to the study of a boundary value problem for second order linear differential equation set on singular cylindrical domain. This problem can be regarded via a natural change of variables as an elliptic abstract differential equation with variable operators coefficients sub...
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| Published in | Afrika mathematica Vol. 30; no. 3-4; pp. 551 - 562 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.06.2019
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1012-9405 2190-7668 |
| DOI | 10.1007/s13370-019-00665-4 |
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| Abstract | The present work is devoted to the study of a boundary value problem for second order linear differential equation set on singular cylindrical domain. This problem can be regarded via a natural change of variables as an elliptic abstract differential equation with variable operators coefficients subject to some anti-periodic conditions. The complete study of this abstract version allows us to establish some interesting regularity results for our problem. The study is performed in the framework of Hölder spaces. |
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| AbstractList | The present work is devoted to the study of a boundary value problem for second order linear differential equation set on singular cylindrical domain. This problem can be regarded via a natural change of variables as an elliptic abstract differential equation with variable operators coefficients subject to some anti-periodic conditions. The complete study of this abstract version allows us to establish some interesting regularity results for our problem. The study is performed in the framework of Hölder spaces. |
| Author | Kostić, Marko Chaouchi, Belkacem |
| Author_xml | – sequence: 1 givenname: Belkacem surname: Chaouchi fullname: Chaouchi, Belkacem email: chaouchicukm@gmail.com organization: Laboratoire de l’Energie et des Systèmes Intelligents, Khemis Miliana University – sequence: 2 givenname: Marko surname: Kostić fullname: Kostić, Marko organization: Faculty of Technical Sciences, University of Novi Sad |
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| Cites_doi | 10.1016/0022-247X(84)90234-8 10.1007/s00009-012-0181-9 10.1619/fesi.47.423 10.1016/j.jmaa.2009.05.010 |
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| Copyright | African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2019 Copyright Springer Nature B.V. 2019 |
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| Keywords | 34K30 Abstract differential equations of second order Variable operator coefficients 34G10 47D03 Hölder spaces 35J25 Anti-periodic boundary conditions |
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| References | Belhamiti, Labbas, Lemrabet, Medeghri (CR4) 2009; 358 Chaouchi (CR3) 2013; 199 Yagi (CR9) 1977; 14 CR6 Chaouchi, Labbas, Sadallah (CR2) 2013; 10 Tanabe (CR8) 1979 Favini, Labbas, Maingot, Tanabe, Yagi (CR5) 2004; 47 Acquistapace, Terreni (CR1) 1984; 99 Sadallah (CR7) 2014; 56 665_CR6 BK Sadallah (665_CR7) 2014; 56 P Acquistapace (665_CR1) 1984; 99 H Tanabe (665_CR8) 1979 A Favini (665_CR5) 2004; 47 B Chaouchi (665_CR3) 2013; 199 A Yagi (665_CR9) 1977; 14 B Chaouchi (665_CR2) 2013; 10 O Belhamiti (665_CR4) 2009; 358 |
| References_xml | – volume: 99 start-page: 9 issue: 1 year: 1984 end-page: 64 ident: CR1 article-title: Some existence and regularity results for abstract non-autonomous parabolic equations publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(84)90234-8 – year: 1979 ident: CR8 publication-title: Equations of Evolution, Monographs and Studies in Mathematics 6 – volume: 10 start-page: 157 issue: 1 year: 2013 end-page: 175 ident: CR2 article-title: Laplace equation on a domain with a cuspidal point in little Hölder spaces publication-title: Mediterr. J. Math. doi: 10.1007/s00009-012-0181-9 – volume: 47 start-page: 423 issue: 3 year: 2004 end-page: 452 ident: CR5 article-title: On the solvability and the maximal regularity of complete abstract differential equations of elliptic type publication-title: Funkc. Ekvacioj doi: 10.1619/fesi.47.423 – ident: CR6 – volume: 56 start-page: 157 issue: 1 year: 2014 end-page: 169 ident: CR7 article-title: Study of a parabolic problem in a conical domain publication-title: Math. J. Okayama Univ. – volume: 199 start-page: 1 year: 2013 end-page: 7 ident: CR3 article-title: Solvability of second-order boundary-value problems on non-smooth cylindrical domains publication-title: Electron. J. Differ. Equ. – volume: 14 start-page: 557 issue: 3 year: 1977 end-page: 568 ident: CR9 article-title: On the abstract evolution equation of parabolic type publication-title: Osaka J. Math. – volume: 358 start-page: 457 issue: 2 year: 2009 end-page: 484 ident: CR4 article-title: Transmission problems in a thin layer set in the framework of the Hölder spaces: Resolution and impedance concept publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2009.05.010 – volume-title: Equations of Evolution, Monographs and Studies in Mathematics 6 year: 1979 ident: 665_CR8 – volume: 99 start-page: 9 issue: 1 year: 1984 ident: 665_CR1 publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(84)90234-8 – volume: 199 start-page: 1 year: 2013 ident: 665_CR3 publication-title: Electron. J. Differ. Equ. – ident: 665_CR6 – volume: 56 start-page: 157 issue: 1 year: 2014 ident: 665_CR7 publication-title: Math. J. Okayama Univ. – volume: 14 start-page: 557 issue: 3 year: 1977 ident: 665_CR9 publication-title: Osaka J. Math. – volume: 10 start-page: 157 issue: 1 year: 2013 ident: 665_CR2 publication-title: Mediterr. J. Math. doi: 10.1007/s00009-012-0181-9 – volume: 358 start-page: 457 issue: 2 year: 2009 ident: 665_CR4 publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2009.05.010 – volume: 47 start-page: 423 issue: 3 year: 2004 ident: 665_CR5 publication-title: Funkc. Ekvacioj doi: 10.1619/fesi.47.423 |
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| Title | An efficient abstract method for the study of an initial boundary value problem on singular domain |
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