Carlos M. Guzm'an

activity

20162026

most citedOn the inhomogeneous NLS with inverse-square potential

17 citations · 43 across the 8 of their papers we have counts for

collaborators

12 papers

math.NA2026

Numerical Analysis for a Nonlinear Coupled Thermoelastic System with Acoustic Boundary Conditions

Adriano A. Alcântara, Bruno A. Carmo, Juan B. Límaco +1

This paper presents the first $L^{2}$ -norm error analysis for a nonlinear thermoelastic system with acoustic boundary conditions. The model involves three coupled variables: the acou…

math.AP2021

Scattering for the non-radial inhomogenous biharmonic NLS equation

Luccas Campos, Carlos M. Guzmán

We consider the focusing inhomogeneous biharmonic nonlinear Schrödinger equation in $H^{2} (R^{N})$ , \begin{equation} iu_t + Δ^2 u - |x|^{-b}|u|^αu=0 \end{equation} when $b > 0…

math.AP2021

Some remarks on the inhomogeneous biharmonic NLS equation

Carlos M. Guzmán, Ademir Pastor

We consider the inhomogeneous biharmonic nonlinear Schrödinger equation $i u_{t} + Δ^{2} u + λ ∣ x ∣^{- b} ∣ u ∣^{α} u = 0,$ where $λ = \pm 1$ and $α$ , $b > 0$ . In the subctritical case, we improve…

math.AP2021★ 17 cited

On the inhomogeneous NLS with inverse-square potential

Luccas Campos, Carlos M. Guzmán

We consider the inhomogeneous nonlinear Schrödinger equation with inverse-square potential in $R^{N}$ $$ i u_t + \mathcal{L}_a u+λ|x|^{-b}|u|^αu = 0,\;\;\mathcal{L}_a=Δ-\fra…

math.AP2021

Scattering for the non-radial energy-critical inhomogeneous NLS

Carlos M. Guzmán, Jason Murphy

We prove scattering below the ground state threshold for an energy-critical inhomogeneous nonlinear Schrödinger equation in three space dimensions. In particular, we extend results…

math.AP2020★ 1 cited

Global well-posedness and critical norm concentration for inhomogeneous biharmonic NLS

Mykael Cardoso, Carlos M. Guzmán, Ademir Pastor

We consider the inhomogeneous biharmonic nonlinear Schrödinger (IBNLS) equation in $R^{N}$ , $i \partial_{t} u + Δ^{2} u - ∣ x ∣^{- b} ∣ u ∣^{2 σ} u = 0,$ where $σ > 0$ and $b > 0$ . We firs…

math.AP2020★ 2 cited

Scattering below the ground state for the intercritical non-radial inhomogeneous NLS

Mykael Cardoso, Luiz Gustavo Farah, Carlos M. Guzmán +1

We consider the focusing inhomogeneous nonlinear Schrödinger equation \[ i\partial_t u + Δu + |x|^{-b}|u|^αu = 0\quad\text{on}\quad\mathbb{R}\times\mathbb{R}^N, \] with $N \geq 2$ ,…

math.AP2020★ 11 cited

On well-posedness and concentration of blow-up solutions for the intercritical inhomogeneous NLS equation

Mykael Cardoso, Luiz Gustavo Farah, Carlos M. Guzmán

We consider the focusing inhomogeneous nonlinear Schrödinger (INLS) equation in $R^{N}$ $i \partial_{t} u + Δ u + ∣ x ∣^{- b} ∣ u ∣^{2 σ} u = 0,$ where $N \geq 2$ and $σ$ , $b > 0$ . We f…

math.AP2019

On the inhomogeneous biharmonic nonlinear Schrödinger equation: local, global and stability results

Carlos M. Guzmán, Ademir Pastor

We consider the inhomogeneous biharmonic nonlinear Schrödinger equation (IBNLS) $i u_{t} + Δ^{2} u + λ ∣ x ∣^{- b} ∣ u ∣^{α} u = 0,$ where $λ = \pm 1$ and $α$ , $b > 0$ . We show local and global wel…

math.AP2017★ 12 cited

Scattering for the radial focusing INLS equation in higher dimensions

Luiz Gustavo Farah, Carlos M. Guzmán

We consider the inhomogeneous nonlinear Schrödinger equation $i u_{t} + Δ u + ∣ x ∣^{- b} ∣ u ∣^{α} u = 0,$ where $\frac{4 - 2 b}{N} < α < \frac{4 - 2 b}{N - 2}$ (when $N = 2$ , $\frac{4 - 2 b}{N} < α < \infty$ ) a…

math.AP2016

Scattering for the radial 3D cubic focusing inhomogeneous nonlinear Schrödinger equation

Luiz Farah, Carlos Guzmán

The purpose of this work is to study the 3D focusing inhomogeneous nonlinear Schrödinger equation $i u_{t} + Δ u + ∣ x ∣^{- b} ∣ u ∣^{2} u = 0,$ where $0 < b < 1/2$ . Let $Q$ be the ground state…

math.AP2016

On well posedness for the inhomogeneous nonlinear Schrödinger equation

Carlos M. Guzmán

The purpose of this paper is to study well-posedness of the initial value problem (IVP) for the inhomogeneous nonlinear Schrödinger equation (INLS) $$ i u_t +Δu+λ|x|^{-b}|u|^αu = 0…