Theoretical aspects of wave propagation for Biot's consolidation problem
- Autores: Hélène Barucq, Monique Madaune-Tort, P. Saint-Macary
- Localización: VIII Journées Zaragoza-Pau de Mathématiques Appliquées et de Statistiques / coord. por Manuel Pedro Palacios Latasa, David Trujillo, Juan José Torrens Iñigo, Monique Madaune-Tort, María Cruz López de Silanes Busto, Gerardo Sanz Sáiz, 2003, ISBN 84-7733-720-9, págs. 449-458
- Idioma: inglés
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Resumen
We consider a coupled system of mixed hyperbolic-parabolic type which describes the Biot consolidation model in poro-elasticity as well as a coupled quasi-static problem in thermoelasticity. In this work, we intend to develop the existence-uniqueness theory for the multi-dimensional systems in the linear case using classical functional arguments in the Sobolev background. For the consolidation model, our approach involves Galerkin approximations to establish the existence of a solution to the problem while we prove that the thermo-elastic and the quasi-static systems are limit cases of the consolidation model. The treatment of the uniqueness is based on an energy inequality even if, in the quasi-static system, it requires some adjustments because of a lack of regularity.
