In this article the following system is investigated:
where is a bounded open set with sufficiently smooth boundary , the maps and are monotone and represent the interior and boundary dissipation, the Nemytski operators , , , , model the interior and boundary sources respectively.
The authors give conditions for , and , under which the problem (1) has unique global weak solution . The exponential and algebraic uniform decay rates of the finite energy are established. The authors prove a blow up result for weak solutions of (1) with nonnegative initial energy.