R. Freire

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math.AP2026

Error bounds for Physics Informed Neural Networks in Generalized KdV Equations placed on unbounded domains

Ricardo Freire, Claudio Muñoz, Nicolás Valenzuela

In this paper we study a rigorous setting for the numerical approximation via deep neural networks of the generalized Korteweg-de Vries (gKdV) model in one dimension, for subcritic…

math.AP2025

On the asymptotic dynamics for the $L^{2}$ -supercritical gKDV equation

Ricardo Freire, Claudio Muñoz

We study the $L^{2}$ -supercritical generalized Korteweg-de Vries equation (gKdV) with nonlinearities $p > 5$ . While local well-posedness in $H^{1}$ is classical, the long-time dynamics i…

math.AP2025

Existence and Nonexistence Breaking Results For a Weighted Elliptic Problem in Half-Space

J. M. Do Ó, R. F. Freire, J. Giacomoni +1

In this paper we study the problem $- div (ρ (x_{N}) \nabla u) = a ∣ u ∣^{p - 2} u$ in $R_{+}^{N}$ , $- \partial u / \partial x_{N} = b ∣ u ∣^{q - 2} u$ in $R^{N - 1}$ where $a,b \in \mat…

math.AP2025

The Cauchy problem for nonlinear dispersive models of long internal waves in the presence of the Coriolis force

Ricardo Freire, Thyago S. R. Santos

We investigate models of dispersive long internal waves with rotational effects, specifically the Benjamin-Ono (BO) and intermediate long wave (ILW) equations modified by the prese…

Error bounds for Physics Informed Neural Networks in Generalized KdV Equations placed on unbounded domains

On the asymptotic dynamics for the L2-supercritical gKDV equation

Existence and Nonexistence Breaking Results For a Weighted Elliptic Problem in Half-Space

The Cauchy problem for nonlinear dispersive models of long internal waves in the presence of the Coriolis force

On the asymptotic dynamics for the $L^{2}$ -supercritical gKDV equation