الخلاصة:
In this work, we were interested in studying the existence and stability of a general
model of evolution equations with a delay term. By the theory of semi-groups and under
appropriate conditions on the delayed damping term, we established the global existence
and the exponential stability of linear and non-linear evolution systems with a constant
delay first and then with a variable and multiple delay term considering a local Lipshitz
source term. The exponential stability of the solution was obtained directly from the
Duhamel formula of the solution in the three cases cited.
The research aims to understand how delays affect the behaviour and stability of
these systems. We terminated this work by illustrating the results obtained with some
applications.
