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Electronic Journal: Southwest Journal of Pure and Applied Mathematics

Internet: http://rattler.cameron.edu/swjpam.html

ISSN 1083-0464

Issue 2, December, 2003, pp. 26–35.

Submitted: December 24, 2002. Published: December 31 2003.

NON-AUTONOMOUS INHOMOGENEOUS BOUNDARY

CAUCHY PROBLEMS AND RETARDED EQUATIONS

M. Filali and M. Moussi

Abstract. In this paper we prove the existence and the uniqueness of classical solution of non-autonomous inhomogeneous boundary Cauchy problems, this solution is given by a variation of constants formula. Then, we apply this result to show the existence of solution of a retarded equation.

A.M.S. (MOS) Subject Classification Codes.

34G10; 47D06

Key Words and Phrases.

Boundary Cauchy problem, Evolution families,

Clas-sical solution, Wellposedness, Variation of constants formula, Retarded equation

Department of Mathematics, Faculty of Sciences, Oujda, Morocco E-mail Address: [email protected]

[email protected] c

2003 Cameron University

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