Existencia, unicidad y estabilidad de la solución a la ecuación termoelástica generalizada.
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| Title: | Existencia, unicidad y estabilidad de la solución a la ecuación termoelástica generalizada. |
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| Authors: | De-la-Cruz, Josermi1,2 j.delacruz@ce.pucmm.edu.do, Toribio-Milane, Juan1 jtoribio34@uasd.edu.do |
| Source: | Latin-American Journal of Physics Education. Jun2024, Vol. 18 Issue 2, p1-6. 6p. |
| Subject Terms: | Exponential stability, Stability theory, Hypothesis |
| Abstract (English): | In this article, the existence and uniqueness of the solution to the thermoelastic problem in its general form are analyzed, based on the theory of strongly continuous operators originated by Hille and Yosida [1, 2] on the study of contractive semigroups. It will be shown that the thermoelastic operator is a generator of a C0-semigroup of contractions, specifically using the Liu-Zheng theorem that simplifies the requirements that the operator must satisfy to prove that it is a generator. To do this, it is proved that it is a dissipative operator with a dense domain and that its resolvent has zero as an element. In addition, the exponential stability of the solution will be studied, which is useful to understand the asymptotic behavior of the C0-semigroup in a long time. This will be demonstrated by verifying the hypotheses of Gearhart's theorem in the thermoelastic operator. [ABSTRACT FROM AUTHOR] |
| Abstract (Spanish): | En este artículo se analizan la existencia y unicidad de la solución al problema termoelástico en su forma general, apoyándose en la teoría de operadores fuertemente continuos originada por Hille y Yosida [1, 2] sobre el estudio de semigrupos contractivos. Se demostrará que el operador termoelástico es generador de un C0-semigupo de contracciones, utilizando específicamente el teorema de Liu-Zheng que simplifica las exigencias que debe satisfacer el operador para probar que es generador. Para ello se prueba que es un operador disipativo con dominio denso y que su resolvente tiene a cero como elemento. Además, se estudiará la estabilidad exponencial de la solución, lo cual resulta útil para comprender el comportamiento asintótico del C0-semigrupo en un tiempo prolongado. Esto se demostrará verificándose las hipótesis del teorema de Gearhart en el operador termoelástico. [ABSTRACT FROM AUTHOR] |
| Copyright of Latin-American Journal of Physics Education is the property of Latin-American Physics Education Network 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: | Education Research Complete |
| FullText | Links: – Type: pdflink Text: Availability: 0 |
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| Header | DbId: ehh DbLabel: Education Research Complete An: 182357906 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Existencia, unicidad y estabilidad de la solución a la ecuación termoelástica generalizada. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22De-la-Cruz%2C+Josermi%22">De-la-Cruz, Josermi</searchLink><relatesTo>1,2</relatesTo><i> j.delacruz@ce.pucmm.edu.do</i><br /><searchLink fieldCode="AR" term="%22Toribio-Milane%2C+Juan%22">Toribio-Milane, Juan</searchLink><relatesTo>1</relatesTo><i> jtoribio34@uasd.edu.do</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Latin-American+Journal+of+Physics+Education%22">Latin-American Journal of Physics Education</searchLink>. Jun2024, Vol. 18 Issue 2, p1-6. 6p. – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Exponential+stability%22">Exponential stability</searchLink><br /><searchLink fieldCode="DE" term="%22Stability+theory%22">Stability theory</searchLink><br /><searchLink fieldCode="DE" term="%22Hypothesis%22">Hypothesis</searchLink> – Name: Abstract Label: Abstract (English) Group: Ab Data: In this article, the existence and uniqueness of the solution to the thermoelastic problem in its general form are analyzed, based on the theory of strongly continuous operators originated by Hille and Yosida [1, 2] on the study of contractive semigroups. It will be shown that the thermoelastic operator is a generator of a C0-semigroup of contractions, specifically using the Liu-Zheng theorem that simplifies the requirements that the operator must satisfy to prove that it is a generator. To do this, it is proved that it is a dissipative operator with a dense domain and that its resolvent has zero as an element. In addition, the exponential stability of the solution will be studied, which is useful to understand the asymptotic behavior of the C0-semigroup in a long time. This will be demonstrated by verifying the hypotheses of Gearhart's theorem in the thermoelastic operator. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Abstract (Spanish) Group: Ab Data: En este artículo se analizan la existencia y unicidad de la solución al problema termoelástico en su forma general, apoyándose en la teoría de operadores fuertemente continuos originada por Hille y Yosida [1, 2] sobre el estudio de semigrupos contractivos. Se demostrará que el operador termoelástico es generador de un C0-semigupo de contracciones, utilizando específicamente el teorema de Liu-Zheng que simplifica las exigencias que debe satisfacer el operador para probar que es generador. Para ello se prueba que es un operador disipativo con dominio denso y que su resolvente tiene a cero como elemento. Además, se estudiará la estabilidad exponencial de la solución, lo cual resulta útil para comprender el comportamiento asintótico del C0-semigrupo en un tiempo prolongado. Esto se demostrará verificándose las hipótesis del teorema de Gearhart en el operador termoelástico. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Latin-American Journal of Physics Education is the property of Latin-American Physics Education Network 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: Languages: – Code: spa Text: Spanish PhysicalDescription: Pagination: PageCount: 6 StartPage: 1 Subjects: – SubjectFull: Exponential stability Type: general – SubjectFull: Stability theory Type: general – SubjectFull: Hypothesis Type: general Titles: – TitleFull: Existencia, unicidad y estabilidad de la solución a la ecuación termoelástica generalizada. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: De-la-Cruz, Josermi – PersonEntity: Name: NameFull: Toribio-Milane, Juan IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2024 Type: published Y: 2024 Identifiers: – Type: issn-print Value: 18709095 Numbering: – Type: volume Value: 18 – Type: issue Value: 2 Titles: – TitleFull: Latin-American Journal of Physics Education Type: main |
| ResultId | 1 |
