DECAYS FOR KELVIN--VOIGT DAMPED WAVE EQUATIONS I: THE BLACK BOX PERTURBATIVE METHOD.
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| Title: | DECAYS FOR KELVIN--VOIGT DAMPED WAVE EQUATIONS I: THE BLACK BOX PERTURBATIVE METHOD. |
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| Authors: | BURQ, NICOLAS1 nicolas.burq@universite-paris-saclay.fr |
| Source: | SIAM Journal on Control & Optimization. 2020, Vol. 58 Issue 4, p1893-1905. 13p. |
| Subjects: | Resolvents (Mathematics), Wave equation, Mathematics, Boxes |
| Abstract: | We show in this article how perturbative approaches from N. Burq and M. Hitrik [Math. Res. Lett., 14 (2007), pp. 35--47] and the black box strategy from N. Burq and M. Zworski [J. Amer. Math. Soc., 17 (2004), pp. 443--471] allow us to obtain decay rates for Kelvin--Voigt damped wave equations from quite standard resolvent estimates: Carleman estimates or geometric control estimates for Helmoltz equation; Carleman or other resolvent estimates for the Helmoltz equation. Though in this context of Kelvin--Voigt damping, such an approach is unlikely to allow for the optimal results when additional geometric assumptions are considered, it turns out that using this method, we can obtain the usual logarithmic decay which is optimal in general cases. We also present some applications of this approach giving decay rates in some particular geometries (tori). [ABSTRACT FROM AUTHOR] |
| Copyright of SIAM Journal on Control & Optimization is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 147613079 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: DECAYS FOR KELVIN--VOIGT DAMPED WAVE EQUATIONS I: THE BLACK BOX PERTURBATIVE METHOD. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22BURQ%2C+NICOLAS%22">BURQ, NICOLAS</searchLink><relatesTo>1</relatesTo><i> nicolas.burq@universite-paris-saclay.fr</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22SIAM+Journal+on+Control+%26+Optimization%22">SIAM Journal on Control & Optimization</searchLink>. 2020, Vol. 58 Issue 4, p1893-1905. 13p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Resolvents+%28Mathematics%29%22">Resolvents (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Wave+equation%22">Wave equation</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics%22">Mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Boxes%22">Boxes</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We show in this article how perturbative approaches from N. Burq and M. Hitrik [Math. Res. Lett., 14 (2007), pp. 35--47] and the black box strategy from N. Burq and M. Zworski [J. Amer. Math. Soc., 17 (2004), pp. 443--471] allow us to obtain decay rates for Kelvin--Voigt damped wave equations from quite standard resolvent estimates: Carleman estimates or geometric control estimates for Helmoltz equation; Carleman or other resolvent estimates for the Helmoltz equation. Though in this context of Kelvin--Voigt damping, such an approach is unlikely to allow for the optimal results when additional geometric assumptions are considered, it turns out that using this method, we can obtain the usual logarithmic decay which is optimal in general cases. We also present some applications of this approach giving decay rates in some particular geometries (tori). [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of SIAM Journal on Control & Optimization is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1137/19M1259080 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 13 StartPage: 1893 Subjects: – SubjectFull: Resolvents (Mathematics) Type: general – SubjectFull: Wave equation Type: general – SubjectFull: Mathematics Type: general – SubjectFull: Boxes Type: general Titles: – TitleFull: DECAYS FOR KELVIN--VOIGT DAMPED WAVE EQUATIONS I: THE BLACK BOX PERTURBATIVE METHOD. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: BURQ, NICOLAS IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 08 Text: 2020 Type: published Y: 2020 Identifiers: – Type: issn-print Value: 03630129 Numbering: – Type: volume Value: 58 – Type: issue Value: 4 Titles: – TitleFull: SIAM Journal on Control & Optimization Type: main |
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