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In this paper, we study the asymptotic behavior of global solutions of the equation ut = ∆u + e |∇u| in the annulus Br,R, u(x, t) = 0 on ∂Br and u(x, t) = M ≥ 0 on ∂BR. It is proved that there exists a constant Mc > 0 such that the problem admits a unique steady state if and only if M ≤ Mc. When M < Mc, the global solution converges in C 1 (Br,R) to the unique regular steady state. When M = Mc, the global solution converges in C(Br,R) to the unique singular steady state, and the blowup rate indoi:10.14232/ejqtde.2012.1.39 fatcat:z6skvpulwngrtpotzobyvq6sg4