Temporal Asymptotic Behavior of Solutions of the Benjamin-ono-burgers Equation

We study certain similarity solutions of the Benjamin-Ono-Burgers (BOB) equation and their role in the asymptotic behavior of the general solution. For small initial data in L 1 (R) we prove that a solution of the BOB equation exists in BC(R + ; L 1 (R)) and depends continuously on its initial data. Results about existence, uniqueness, regularity, and spatial asymptotics of solutions of a similarity reduction of the BOB equation are proved. Furthermore, the solutions of the BOB equation are proved to converge as t ! 1 to appropriate similarity solutions faster than the typically sharp rate of decay of the solutions.