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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.

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E-PrintsUCM  

Autor(es)

Díaz Díaz, Jesús Ildefonso -  Casal, Alfonso C. -  Vegas Montaner, José Manuel - 

Id.: 55287214

Idioma: spa  - 

Versión: 1.0

Estado: Final

Tipo:  application/pdf - 

Palabras claveEcuaciones diferenciales - 

Tipo de recurso: Artículo  -  PeerReviewed  - 

Tipo de Interactividad: Expositivo

Nivel de Interactividad: muy bajo

Audiencia: Estudiante  -  Profesor  -  Autor  - 

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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