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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.22 no.2 Antofagasta Aug. 2003

http://dx.doi.org/10.4067/S0716-09172003000200005 

Proyecciones
Vol. 22, N o 2, pp. 145-159, August 2003.
Universidad Católica del Norte
Antofagasta - Chile

NON - AUTONOMOUS INHOMOGENEOUS
BOUNDARY CAUCHY PROBLEMS AND
RETARDED EQUATIONS

M. FILALI AND M. MOUSSI
Universidad de Mohamed I, MOROCCO

Abstract
In this paper we prove the existence and the uniqueness of the clas-sical
solution of non-autonomous inhomogeneous boundary Cauchy
problems, and that this solution is given by a variation of constants
formula. This result is applied to show the existence of solutions of a
retarded equation.


subjclass : 34G10; 47D06
keywords : Boundary Cauchy problem, evolution families, clas-sical
solution, well-posedness, variation of constants formula, retarded
equation.

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M. Filali
Department of Mathematics
Faculty of Sciences
University Mohamed I
P. O. Box 524
60000 Oujda
Morocco
filali@sciences.univ-oujda.ac.ma

and

M. Moussi
Department of Mathematics
Faculty of Sciences
University Mohamed I
P. O. Box 524
60000 Oujda
Morocco
moussi@sciences.univ-oujda.ac.ma

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