On the double Moore–Gibson–Thompson system of thermoviscoelasticity
In this paper, we address the system made by two coupled one-dimensional Moore–Gibson–Thompson equations (···u + aü - ß·u_xx - ¿u_xx = p(a·w_x + ¨w_x)) i (···w + ^a¨w - ^ß·w_xx - ^¿w_xx = ^p( ^a·u_xx + ü_x)) arising in the description of thermoviscoelastic materials. Here, a, ß, ¿, ^a, ^ß, ^¿ > 0...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| 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:2117/422886 |
| Acceso en línea: | https://hdl.handle.net/2117/422886 https://dx.doi.org/10.1111/sapm.12784 |
| Access Level: | acceso abierto |
| Palabra clave: | Exponential stability Moore–Gibson–Thompson system Solution semigroup Thermoviscoelasticity Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències |
| Sumario: | In this paper, we address the system made by two coupled one-dimensional Moore–Gibson–Thompson equations (···u + aü - ß·u_xx - ¿u_xx = p(a·w_x + ¨w_x)) i (···w + ^a¨w - ^ß·w_xx - ^¿w_xx = ^p( ^a·u_xx + ü_x)) arising in the description of thermoviscoelastic materials. Here, a, ß, ¿, ^a, ^ß, ^¿ > 0 while p^p > 0. When both the MGT equations lie in the subcritical regime, that is, ß - ¿/a > 0 and ^ß - ^¿/^a > 0 we prove that the system generates an exponentially stable solution semigroup. This improves some recent results in the literature, where the exponential stability is attained only within either a stronger condition than subcriticality of both equations, or when a and ^a are sufficiently close. The key idea is to deduce the exponential stability from that of a related system, made by two coupled equations of the viscoelasticity type. The latter result has also an independent interest. |
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