The influence of nonlocal nonlinearities on the long time behavior of solutions of Burgers' equation
We study the long time behavior of solutions of Burgers's equation with nonlocal nonlinearities: ut uxx + euux + \(a\\u(-, 0llP_' + b)u, 0 < x < 1 , a, e € M, b > 0, p > 1, subject to u( 0, t) = w(l , t) = 0. A stability-instability analysis is given in some detail, and some finite time blow up results are given.