5 papers
On decay of the solutions for the dispersion generalized-Benjamin-Ono and Benjamin-Ono equations
Alysson Cunha
We show that uniqueness results of the kind those obtained for KdV and Schrödinger equations ([7], [28]), are not valid for the dispersion generalized-Benjamin-Ono equation in the…
On uniqueness results for the Benjamin equation
Alysson Cunha
We prove that the uniqueness results obtained in \cite{urrea} for the Benjamin equation, cannot be extended for any pair of non-vanishing solutions. On the other hand, we study uni…
Persistence properties for the dispersion generalized BO-ZK equation in weighted anisotropic Sobolev spaces
Alysson Cunha, Ademir Pastor
In this paper we study the initial-value problem associated with the dispersion generalized-Benjamin-Ono-Zakharov-Kuznetsov equation, $$ u_{t}+D^{a+1}_x \partial_{x}u+u_{xyy}+uu_{x…
The Cauchy Problem for Dissipative Benjamin-Ono equation in Weighted Sobolev spaces
Alysson Cunha
We study the well-posedness in weighted Sobolev spaces, for the initial value problem (IVP) associated with the dissipative Benjamin-Ono (dBO) equation. We establish persistence pr…
The IVP for the Kuramoto-Sivashinsky equation in low regularity Sobolev spaces
Alysson Cunha, Eduardo Alarcon
In this work, we study the initial-value problem associated with the Kuramoto-Sivashinsky equation. We show that the associated initial value problem is locally and globally well-p…