Detalles del recurso
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Descripción: Blow-up phenomena are analyzed for both the delay-differential equation (DDE) u'(t) = B'(t)u(t - tau), and the associated parabolic PDE (PDDE) partial derivative(t)u=Delta u+B'(t)u(t-tau,x), where B : [0, tau] -> R is a positive L(1) function which behaves like 1/vertical bar t - t*vertical bar(alpha), for some alpha is an element of (0, 1) and t* is an element of (0,tau). Here B' represents its distributional derivative. For initial functions satisfying u(t* - tau) > 0, blow up takes place as t NE arrow t* and the behavior of the solution near t* is given by u(t) similar or equal to B(t)u(t - tau), and a similar result holds for the PDDE. The extension to some nonlinear equations is also studied: we use the Alekseev's formula (case of nonlinear (DDE)) and comparison arguments (case of nonlinear (PDDE)). The existence of solutions in some generalized sense, beyond t = t* is also addressed. This results is connected with a similar question raised by A. Friedman and J. B. McLeod in 1985 for the case of semilinear parabolic equations.
Autor(es): Díaz Díaz, Jesús Ildefonso - Casal, Alfonso C. - Vegas Montaner, José Manuel -
Id.: 55287214
Idioma:
spa
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Versión: 1.0
Estado: Final
Tipo: application/pdf -
Palabras clave: Ecuaciones diferenciales -
Tipo de recurso:
Artículo
- PeerReviewed
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Tipo de Interactividad: Expositivo
Nivel de Interactividad: muy bajo
Audiencia:
Estudiante
- Profesor
- Autor
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Estructura: Atomic
Coste: no
Copyright: sí
: info:eu-repo/semantics/embargoedAccess
Formatos: application/pdf -
Requerimientos técnicos: Browser: Any -
Relación:
[References] http://www.dynamicpublishers.com/DSA/dsa18pdf/03-DSA-CY-3-Casal.pdf
[References] http://eprints.ucm.es/15136/
Fecha de contribución: 09-may-2012
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