6 papers
Explicit Analytical Representations for the Schwarzschild Radial Equation via Hypergeometric and Frobenius Expansions
J. G. R. Valangelis, Ailton C. Nascimento, Helder A. S. Costa
The massive Klein-Gordon equation on the Schwarzschild exterior reduces to a radial differential equation of confluent-Heun type. We present its exact reduction by rigorously retai…
Unique continuation for the periodic Benjamin-Bona-Mahony equation
Roberto de A. Capistrano Filho, Victor Hugo Gonzalez Martinez, Ailton Campos do Nascimento
We prove unique continuation for the real periodic Benjamin--Bona--Mahony equation in the energy space: a solution that equals a constant on a nonempty space--time strip is that co…
On the local well-posedness of the Benjamin-Ono-Zakharov-Kuznetsov equation
Ailton C. Nascimento
We study the Cauchy problem for the Benjamin--Ono--Zakharov--Kuznetsov equation on . Following the strategy of Kenig and Ziesler, we establish new maximal-function est…
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…
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…
On the Propagation of Regularity of Solutions to the KdV Equation on the positive Half-line
Márcio Cavalcante, Aílton 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…