We study the long-time behavior of solutions of Burgers' equation with nonlocal nonlinearities u t = u xx + "uu x + 1 2 ? aku(; t)k p?1 + b u, 0 < x < 1, a; " 2 , b > 0, p > 1, subject to u(0; t) = u(1; t) = 0. A stability{instability analysis is given in some detail, and some nite-time blow-up results are given.
