Spatial Behavior of Solutions in Linear Thermoelasticity with Voids and Three Delay Times
This brief contribution aims to complement a study of well-posedness started by the same authors in 2020, showing—for that same mathematical model—the existence of a domain of influence of external data. The object of investigation, we recall, is a linear thermoelastic model with a porous matrix mod...
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| Format: | Article |
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MDPI AG
2023-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/19/4195 |
| _version_ | 1797575557667356672 |
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| author | Manuela Carini Vittorio Zampoli |
| author_facet | Manuela Carini Vittorio Zampoli |
| author_sort | Manuela Carini |
| collection | DOAJ |
| description | This brief contribution aims to complement a study of well-posedness started by the same authors in 2020, showing—for that same mathematical model—the existence of a domain of influence of external data. The object of investigation, we recall, is a linear thermoelastic model with a porous matrix modeled on the basis of the Cowin–Nunziato theory, and for which the heat exchange phenomena are intended to obey a time-differential heat transfer law with three delay times. We therefore consider, without reporting it explicitly, the (suitably adapted) initial-boundary value problem formulated at that time, as well as some analytical techniques employed to handle it in order to address the uniqueness and continuous dependence questions. Here, a domain of influence theorem is proven, showing the spatial behavior of the solution in a cylindrical domain, by activating the hypotheses that make the model thermodynamically consistent. The theorem, in detail, demonstrates that for a finite time <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>t</mi><mo>></mo><mn>0</mn></mrow></semantics></math></inline-formula>, the assigned external (thermomechanical) actions generate no disturbance outside a bounded domain contained within the cylindrical region of interest. The length of the work is deliberately kept to a minimum, having opted where possible for bibliographic citations in favor of greater reading fluency. |
| first_indexed | 2024-03-10T21:40:14Z |
| format | Article |
| id | doaj.art-db56c75b12f141b787d95b6f096ec88a |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T21:40:14Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-db56c75b12f141b787d95b6f096ec88a2023-11-19T14:44:39ZengMDPI AGMathematics2227-73902023-10-011119419510.3390/math11194195Spatial Behavior of Solutions in Linear Thermoelasticity with Voids and Three Delay TimesManuela Carini0Vittorio Zampoli1DIAM (Department of Environmental Engineering), University of Calabria, via Pietro Bucci, 87036 Arcavacata di Rende, ItalyDIEM (Department of Information and Electrical Engineering and Applied Mathematics), University of Salerno, via Giovanni Paolo II, 84084 Fisciano, ItalyThis brief contribution aims to complement a study of well-posedness started by the same authors in 2020, showing—for that same mathematical model—the existence of a domain of influence of external data. The object of investigation, we recall, is a linear thermoelastic model with a porous matrix modeled on the basis of the Cowin–Nunziato theory, and for which the heat exchange phenomena are intended to obey a time-differential heat transfer law with three delay times. We therefore consider, without reporting it explicitly, the (suitably adapted) initial-boundary value problem formulated at that time, as well as some analytical techniques employed to handle it in order to address the uniqueness and continuous dependence questions. Here, a domain of influence theorem is proven, showing the spatial behavior of the solution in a cylindrical domain, by activating the hypotheses that make the model thermodynamically consistent. The theorem, in detail, demonstrates that for a finite time <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>t</mi><mo>></mo><mn>0</mn></mrow></semantics></math></inline-formula>, the assigned external (thermomechanical) actions generate no disturbance outside a bounded domain contained within the cylindrical region of interest. The length of the work is deliberately kept to a minimum, having opted where possible for bibliographic citations in favor of greater reading fluency.https://www.mdpi.com/2227-7390/11/19/4195linear thermoelasticityvoidsdelay timesdomain of influence |
| spellingShingle | Manuela Carini Vittorio Zampoli Spatial Behavior of Solutions in Linear Thermoelasticity with Voids and Three Delay Times Mathematics linear thermoelasticity voids delay times domain of influence |
| title | Spatial Behavior of Solutions in Linear Thermoelasticity with Voids and Three Delay Times |
| title_full | Spatial Behavior of Solutions in Linear Thermoelasticity with Voids and Three Delay Times |
| title_fullStr | Spatial Behavior of Solutions in Linear Thermoelasticity with Voids and Three Delay Times |
| title_full_unstemmed | Spatial Behavior of Solutions in Linear Thermoelasticity with Voids and Three Delay Times |
| title_short | Spatial Behavior of Solutions in Linear Thermoelasticity with Voids and Three Delay Times |
| title_sort | spatial behavior of solutions in linear thermoelasticity with voids and three delay times |
| topic | linear thermoelasticity voids delay times domain of influence |
| url | https://www.mdpi.com/2227-7390/11/19/4195 |
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