Résumé:
This memoir aims to study two cases of general mixed problems with integral con-
ditions, both classical and non-local.
The memoir begins with an introduction providing background and interest in the
addressed topic, along with mentioning some preliminary concepts useful later on.
In the second chapter, a problem involving a non-local boundary condition for a
parabolic differential equation is addressed. We employ functional analysis method to
prove the existence and uniqueness of the strong solution to the problem.
In the third chapter, our focus shifts to exploring the weak solution of the problem
and proving its existence and uniqueness related to the specific issue, relying on the a
priori estimation method used in the previous chapter for proving uniqueness. As for
the existence of the solution, the Galerkin method is utilized. Finally, a fixed point
argument is used to prove the existence of the local solution to the problem.
