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math.AP2025
The Kawahara equation on star graphs
Márcio Cavalcante, Chulkwang Kwak, José Marques
In this paper, we establish local well-posedness for the Cauchy problem associated with the Kawahara equation on a general metric star graph. Initially, we identify suitable bounda…
math.AP2025
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…
math.AP2025
The Korteweg-de Vries Equation on general star graphs
Márcio Cavalcante, José Marques
In this paper, we establish local well-posedness for the Cauchy problem associated with the Korteweg-de Vries (KdV) equation on a general metric star graph. The graph comprises m +…