| Título: | Finite extinction time property for a delayed linear problem on a manifold without boundary |
| Autores: | Casal, Alfonso C. ; Díaz Díaz, Jesús Ildefonso ; Vegas Montaner, José María |
| Tipo de documento: | texto impreso |
| Editorial: | American Institute of Mathematical Sciences, 2011 |
| Dimensiones: | application/pdf |
| Nota general: |
info:eu-repo/semantics/restrictedAccess info:eu-repo/semantics/openAccess |
| Idiomas: | |
| Palabras clave: | Estado = Publicado , Materia = Ciencias: Matemáticas: Ecuaciones diferenciales , Tipo = Artículo |
| Resumen: |
We prove that the mere presence of a delayed term is able to connect the initial state u0 on a manifold without boundary (here assumed given as the set ?? where ? is an open bounded set in RN ) with the zero state on it and in a finite time even if the dynamics is given by a linear problem. More precisely, we extend the states to the interior of ? as harmonic functions and assume the dynamics given by a dynamic boundary condition of the type ?u ?t (t, x) + ?u ?n (t, x) + b(t)u(t ? ?, x) = 0 on ??, where b : [0, ?) ? R is continuous and ? > 0. Using a suitable eigenfunction expansion, involving the Steklov BVP {??n = 0 in ?, ???n = ?n?n on ??}, we show that if b(t)vanishes on [0, ?] ? [2?, ?) and satisfies some integral balance conditions, then the state u(t, .) corresponding to an initial datum u0(t, ·) = µ(t)?n(·) vanish on ?? (and therefore in ?) for t ? 2?. We also analyze more general types of delayed boundary actions for which the finite extinction phenomenon holds for a much larger class of initial conditions and the associated implicit discretized problem. |
| En línea: | https://eprints.ucm.es/id/eprint/29696/1/155.pdf |
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