Before revision:  In this paper we prove that when the dividend function is positive and concave, then the boundary  tends to 0 as time tends to t_d^- and is non-increasing in a left-hand neighbourhood of t_d.
After revision:  In this paper we prove that when the dividend function is positive and concave, then the boundary is non-increasing in a left-hand neighbourhood of t_d, and tends to 0 as time tends to t_d^- and is non-increasing in a left-hand neighbourhood of t_d.