Stabilization beyond the distributions
نویسنده
چکیده
We prove that for suitable evolution problems, the solution u(t) corresponding to some right hand side term f(t) in V ′ (with V some Hilbert space), only satisfies the stabilization property (f(t) → f∞ in V ′ implies that u(t) → u∞, in V , when t → +∞, with u∞ solution of the associated stationary problem) when the space V is taken strictly larger than the distribution space. This type of problems arise, for instance, in the study of some quasi-stationary viscoelastic shell-like problems in the presence of friction effects. Estabilización más allá de las distribuciones Resumen. Probamos que en ciertos problemas de evolución, la solución correspondiente a adecuados términos del lado derecho f(t) en V ′ (con V cierto espacio de Hilbert), sólo satisface la propiedad de estabilización (f(t)→ f∞ en V ′ implica que u(t)→ u∞, en V , cuando t→ +∞, con u∞ solución del problema estacionario asociado) cuando el espacio V es tomado estrictamente más grande que el espacio de distribuciones. Este tipo de situaciones aparecen, por ejemplo, en el estudio de ciertas formulaciones del estilo de los problemas de estructuras finas viscoelásticas con fricción.
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تاریخ انتشار 2009