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