arXiv subjects

Daniel Oliveira da Silva

Publications and source records attributed to Daniel Oliveira da Silva.

8 recordsLinked to original sources

arXiv2023

Well-posedness for a molecular beam epitaxy model

We study a general molecular beam epitaxy (MBE) equation modeling the epitaxial growth of thin films. We show that, in the deterministic case, the associated Cauchy problem admits a unique smooth solution for all time, given initial data in the space $X_0 = L^{2}(R^{d}) \cap \dot{W}^{1,4}(R^{d})$ with $d = 1, 2$. This improves a recent result by Agélas, who established global existence in $H^{3}(R^{d})$. Moreover, we investigate the local existence and uniqueness of solutions in the space $X_0$ for the stochastic MBE equation, with an additive noise that is white in time and regular in the space variable.

math.AP↗

arXiv2022

On the Radius of Analyticity for a Korteweg-de Vries-Kawahara Equation with a Weakly Damping Term

We consider the Cauchy problem for an equation of Korteweg-de Vries-Kawahara type with initial data in the analytic Gevrey spaces. By using linear, bilinear and trilinear estimates in analytic Bourgain spaces, we establish the local well-posedness for this problem. By using an approximate conservation law, we extend this to a global result in such a way that the radius of analyticity of solutions is uniformly bounded below by a fixed positive number for all time.

math.AP↗

arXiv2021

Gradient Bounds and Coarsening Estimates for Some Molecular Beam Epitaxy Models

We prove global well-posedness for some molecular beam epitaxy models. This requires proving some bounds on the gradient of solutions. We also obtain some global bounds on the roughness of solutions.

math.AP↗

arXiv2020

Global well-posedness for the nonlinear wave equation in analytic Gevrey spaces

We obtain an asymptotic rate of decay for the radius of spatial analyticity of solutions to the nonlinear wave equation with initial data in the analytic Gevrey spaces.

math.AP↗

arXiv2020

Global Well-Posedness for the Fifth-Order Kadomtsev-Petviashvili II Equation in Anisotropic Gevrey Spaces

We show that the fifth-order Kadomtsev-Petviashvili II equation is globally well-posed in an anisotropic Gevrey space, which complements earlier results on the well-posedness of this equation in anisotropic Sobolev spaces.

math.AP↗

arXiv2019

Global Analytic Solutions for the Nonlinear Schrödinger Equation

We prove the existence of global analytic solutions to the nonlinear Schrödinger equation in one dimension for a certain type of analytic initial data in $L^2$.

math.AP↗

arXiv2018

Local Well-Posedness for Generalized Semilinear Black-Scholes Equations

We consider some parabolic equations which are model problems for a variety of nonlinear generalizations to the Black-Scholes equation of mathematical finance. In particular, we prove local well-posedness for the Cauchy problem with initial data in $L^{p}$ spaces.

math.AP↗

arXiv2013

A Remark on Unconditional Uniqueness in the Chern-Simons-Higgs Model

The solution of the Chern-Simons-Higgs model in Lorenz gauge with data for the potential in $H^{s-1/2}$ and for the Higgs field in $H^s \times H^{s-1}$ is shown to be unique in the natural space $C([0,T];H^{s-1/2} \times H^s \times H^{s-1})$ for $s \ge 1$, where $s=1$ corresponds to finite energy. Huh and Oh recently proved local well-posedness for $s > 3/4$, but uniqueness was obtained only in a proper subspace $Y^s$ of Bourgain type. We prove that any solution in $C([0,T];H^{1/2} \times H^1 \times L^2)$ must in fact belong to the space $Y^{3/4+ε}$, hence it is the unique solution obtained by Huh and Oh.

math.AP↗