  The paper deals with a semilinear integrodifferential equation that
characterizes several dissipative models of Viscoelasticity, Biology and
Superconductivity. The initial - boundary problem with Neumann conditions is
analyzed. When the source term F is a linear function, then the explicit
solution is obtained. When F is non linear, some results on existence,
uniqueness and a priori estimates are deduced. As example of physical model the
reaction - diffusion system of Fitzhugh Nagumo is considered.
