2005-Oujda International Conference on Nonlinear Analysis,
Oujda, Morocco.
Electronic Journal of Differential Equations,
Conference 14 (2006), pp. 191-205. 

Title: Non-autonomous inhomogeneous boundary Cauchy problems

Authors: Mohammed Filali (Univ. Mohammed 1er, Oujda, Maroc)
         Belhadj Karim   (Univ. Mohammed 1er, Oujda, Maroc)
 
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.