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.