2005-Oujda International Conference on Nonlinear Analysis, Oujda, Morocco.
Electron. J. Diff. Eqns., Conference 14 (2006), pp. 191-205.

Non-autonomous inhomogeneous boundary Cauchy problems

Mohammed Filali, Belhadj Karim

Abstract:
In this paper we prove existence and uniqueness of classical solutions for the non-autonomous inhomogeneous Cauchy problem
$$\displaylines{ \frac{d}{dt}u(t)=A(t)u(t)+f(t), \quad 0 \leq s\leq t\leq T, \cr L(t)u(t)=\Phi(t)u(t)+g(t) , \quad 0\leq s\leq t\leq T, \cr u(s)=x. }$$
The solution to this problem is obtained by a variation of constants formula.

Published September 20, 2006.
Math Subject Classifications: 34G10, 47D06.
Key Words: Boundary Cauchy problem; evolution families; solution; well posedness; variation of constants formula.

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Mohammed Filali
Département de Mathématiques et Informatique
Faculté des Sciences
Université Mohammed 1er, Oujda, Maroc
email: filali@sciences.univ-oujda.ac.ma
Belhadj Karim
Département de Mathématiques et Informatique
Faculté des Sciences
Université Mohammed 1er, Oujda, Maroc
email: karim@sciences.univ-oujda.ac.ma

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