A reaction-diffusion equation with memory kernel of Jeffreys type and with a balanced bistable
reaction term is considered in a bounded interval of the real line. Taking advantage of the fact that in this case the
integro-differential equation can be transformed into a local partial differential equation, it is proved that there exist
solutions which evolve very slowly in time and maintain a transition layer structure for an exponentially long time
Tε≥ c1 exp(c2/ε) as ε→ 0+,
where ε2 is the diffusion coefficient.
Hence, we extend to reaction-diffusion equations with memory kernel of Jeffreys type the well-known results valid for the classic
Allen-Cahn equation.