Decay of solutions for strain gradient mixtures
We study antiplane shear deformations for isotropic and homogeneous strain gradient mixtures of the Kelvin-Voigt type in a cylinder. Our aim is to analyze the behaviour of the solutions with respect to the time variable when a dissipative structural mechanism is considered. We study three different...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:270778 |
| Acceso en línea: | https://ddd.uab.cat/record/270778 https://dx.doi.org/urn:doi:10.1002/zamm.202200089 |
| Access Level: | acceso abierto |
| Palabra clave: | Strain gradient Mixture Decay PDE |
| Sumario: | We study antiplane shear deformations for isotropic and homogeneous strain gradient mixtures of the Kelvin-Voigt type in a cylinder. Our aim is to analyze the behaviour of the solutions with respect to the time variable when a dissipative structural mechanism is considered. We study three different cases, each at a time. For each case we prove existence and uniqueness of solutions. We obtain the exponential decay of the solutions in the hyperviscosity and viscosity cases. Exponential decay is also expected when the dissipation is generated by the relative velocity (in the generic case, although a particular combination of the constitutive parameters leads to slow decay). These results are proved with the help of the theory of semigroups. |
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