  The initial value problem for an evolution equation of type $v' + Av + BKv =
f$ is studied, where $A:V_A \to V_A'$ is a monotone, coercive operator and
where $B:V_B \to V_B'$ induces an inner product. The Banach space $V_A$ is not
required to be embedded in $V_B$ or vice versa. The operator $K$ incorporates a
Volterra integral operator in time of convolution type with an exponentially
decaying kernel. Existence of a global-in-time solution is shown by proving
convergence of a suitable time discretisation. Moreover, uniqueness as well as
stability results are proved. Appropriate integration-by-parts formulae are a
key ingredient for the analysis.
