On the Asymptotic Behavior of Solutions to the (Generalized) Kadomtsev–Petviashvili–Burgers Equations

We show global existence and sharp results on the asymptotic decay of solutions to the generalized KP equations with a power nonlinearityupuxand with a Burgers-type dissipation in the main direction of propagation appended. Furthermore, we prove that forp * the decay rate of theL2-norm of the solution of these equations is that exhibited by the solution of these same equations linearized around the zero solution and that, forp 2, this also holds for theL∞-norm. This limitation seems due to the presence of a dispersive effect in the transverse direction.