Blow-up for a system ofheat equations with nonlocal sources and absorptions

In this paper we establish the local existence of the nonnegative solution and the finite time blow-up results for the following parabolic system: subject to homogeneous Dirichlet conditions and nonnegative initial data, where p, q, r, s ≥ 1 and a, b > 0. In the situation when the nonnegative solution (u, v) of the above problem blows up in finite time, we show that the blow-up is global and this differs from the local source case. Moreover, it is proved that for the special case r = s = 1, if (u, v) blows up then the limits converge uniformly on compact subsets of Ω, where T* is the blow-up time.