  The diffusion equation is extended by including spatial-temporal memory in
such a manner that the conservation of the concentration is maintained. The
additional memory term gives rise to the formation of non-trivial stationary
solutions. The steady state pattern in an infinite domain is driven by a
competition between conventional particle current and a feedback current. We
give a general criteria for the existence of a non-trivial stationary state.
The applicability of the model is tested in case of a strongly localized, time
independent memory kernel. The resulting evolution equation is exactly solvable
in arbitrary dimensions and the analytical solutions are compared with
numerical simulations. When the memory term offers an spatially decaying
behavior, we find also the exact stationary solution in form of a screened
potential.
