3 papers
math.AP2026
Unique Continuation for Fifth-Order KP Equation and its application to control problems
Roberto de A. Capistrano-Filho, Ailton C. Nascimento
We develop a framework for the fifth-order Kadomtsev--Petviashvili equation on within a mean-zero KP-adapted Sobolev scale. A localized high-orde…
math.AP2025
Long-Time Dynamics of the Zakharov-Kuznetsov Equation
Roberto de A. Capistrano Filho, Ailton Nascimento
This manuscript presents the results of stabilization for the Zakharov--Kuznetsov equation, a two-dimensional Korteweg--de Vries-type equation. We provide rigorous proofs using two…
math.AP2025
On the Propagation of Regularity of Solutions to the KdV Equation on the positive Half-line
Márcio Cavalcante, AÃlton C. Nascimento
We study special regularity properties of solutions to the initial-boundary value problem associated with the Korteweg-de Vries equations posed on the positive half-line. In partic…