Behavior of Solutions of Burgers′ Equation with Nonlocal Boundary Conditions

In this paper, we discuss the long-time behavior of positive solutions of Burgers′ equation ut = uxx + εuux, 0 < x < 1, ε > 0, t > 0 with the nonlocal boundary condition: u(0, t) = 0, ux(1, t) + εu2(1, t) = aup(1, t) (∫10u(x, t) dx)q, where 0 < p < ∞, 0 < q < ∞. Criteria for stability are given. Blowup in finite time for some solutions is shown. General results are discussed.