Continuous dependence and convergence for Moore–Gibson–Thompson heat equation
In this paper, we investigate how the solutions vary when the relaxation parameter, the conductivity rate parameter, or the thermal conductivity parameter change in the case of the Moore-Gibson-Thompson heat equation. In fact, we prove that they can be controlled by a term depending upon the square...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/387399 |
| Acceso en línea: | https://hdl.handle.net/2117/387399 https://dx.doi.org/10.1007/s00707-023-03537-y |
| Access Level: | acceso abierto |
| Palabra clave: | Thermoelasticity Termoelasticitat Classificació AMS::35 Partial differential equations::35B Qualitative properties of solutions Classificació AMS::35 Partial differential equations::35L Partial differential equations of hyperbolic type Classificació AMS::35 Partial differential equations::35Q Equations of mathematical physics and other areas of application Classificació AMS::80 Classical thermodynamics, heat transfer::80A Thermodynamics and heat transfer Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències |
| Sumario: | In this paper, we investigate how the solutions vary when the relaxation parameter, the conductivity rate parameter, or the thermal conductivity parameter change in the case of the Moore-Gibson-Thompson heat equation. In fact, we prove that they can be controlled by a term depending upon the square of the variation of the parameter. These results concern the structural stability of the problem. We also compare the solutions of the MGT equation with the Maxwell-Cattaneo heat conduction equation and the type III heat equation (limit cases for the first two previous parameters) and we show how the difference between the solutions can be controlled by a term depending on the square of the limit parameter. This result gives a measure of the convergence between the solutions for the different theories |
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