Fabio Silva Botelho, PhD

Professor Adjunto, Departamento de Matemática

Universidade Federal de Santa Catarina - UFSC



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Introdução à Análise – 2019-1


Resultados da Primeira avaliação


Matrículas - Notas


16150505 – 8.0

16100815 – 3.0

16250258 – 9.0




Cálculo Variacional


Horário 2019/1 - Tópicos em Cálculo Variacional e Otimização em Espaços de Banach

Terças 18 h – 20 h 30 min

e Quintas 16 h – 18 h 30 min

Sala CFM A 11 – Ambos os dias


Análise Funcional – Curso de Verão – 2019 – Notas de Aula, Listas de Exercícios e resultados da segunda avaliação de 1/3/2019


Análise Funcional Aplicada


Cálculo 1 – notas de aula


Cálculo 1 – 2018-2 - Listas de exercícios -Resultados - REC


Cálculo 2 – 2018-2- Listas de exercícios -Resultados da P-3


PAM – Listas de exercícios


Livros:

Functional Analysis and Applied Optimization in Banach Spaces, Springer 2014.

Book review

Real Analysis and Applications, Springer 2018.


A Classical Description of Variational Quantum Mechanics and Related Models, Nova Science Publishing, 2017.

This work is dedicated in memoriam to David Bohm and Jiddu Krishnamurti


Pre-prints – Physics


1. arXiv:1812.04097 [pdf, ps, other]
A variational formulation for relativistic mechanics based on Riemannian geometry and its application to the quantum mechanics context
Fabio Botelho
Comments: 15 pages, new results based on the Weinberg approach for relativistic mechanics
Subjects: Analysis of PDEs (math.AP)

2. A Variational Formulation for the Relativistic Klein-Gordon Equation


Pre-prints-Applied Mathematics


1. arXiv:1904.12379  [pdf, ps, other

math.NA

On the generalized method of lines and its proximal explicit and hyper-finite difference approaches

Authors: Fabio Botelho

Abstract: This article firstly develops a proximal explicit approach for the generalized method of lines. In such a method, the domain of the PDE in question is discretized in lines and the equation solution is written on these lines as functions of the boundary conditions and domain shape. The main objective of introducing a proximal formulation is to minimize the solution error as a typical parameter… ▽ More

Submitted 7 May, 2019; v1 submitted 28 April, 2019; originally announced April 2019.

Comments: 18 pages, some typos corrected, a new result added

MSC Class: 65N40; 65N06


1.1. arXiv:1904.02286  [pdf, ps, other

math.OC

A primal dual variational formulation and a multi-duality principle for a non-linear model of plates

Authors: Fabio Botelho

Submitted 18 April, 2019; v1 submitted 3 April, 2019; originally announced April 2019.

Comments: 20 pages, some typos corrected, a new result added

MSC Class: 49N15; 74P99

2. arXiv:1903.06014 [pdf, ps, other]
A duality principle for non-convex optimization in Rn
Fabio Botelho
Comments: 13 pages, some typos and errors corrected, in this version all proof details have been provided
Subjects: Optimization and Control (math.OC)
3. arXiv:1902.08811 [pdf, ps, other]
A note on optimization in Rn
Fabio Botelho
Comments: 10 pages
Subjects: Optimization and Control (math.OC)
4. arXiv:1902.04448 [pdf, ps, other]
Existence of solution for an optimal control problem associated to the Ginzburg-Landau system in superconductivity
Fabio Botelho, Eduardo Pandini Barros
Comments: 8 pages
Subjects: Optimization and Control (math.OC)
5. arXiv:1812.04097 [pdf, ps, other]
A variational formulation for relativistic mechanics based on Riemannian geometry and its application to the quantum mechanics context
Fabio Botelho
Comments: 15 pages, new results based on the Weinberg approach for relativistic mechanics
Subjects: Analysis of PDEs (math.AP)
6. arXiv:1809.09575 [pdf, ps, other]
On central fields in the calculus of variations
Fabio Botelho
Comments: 12 pages, typos corrected
Subjects: Optimization and Control (math.OC)
7. arXiv:1804.06283 [pdf, ps, other]
On General Duality Principles for Non-Convex Variational Optimization with Applications to the Ginzburg-Landau System in Superconductivity
Fabio Botelho
Comments: 32 pages, typos corrected, other results added
Subjects: Optimization and Control (math.OC)
8. arXiv:1712.04809 [pdf, ps, other]
A duality principle for a semi-linear model in micro-magnetism
Fabio Botelho
Comments: 7 pages
Subjects: Optimization and Control (math.OC)
9. arXiv:1712.03552 [pdf, ps, other]
On the numerical solution of non-linear first order ordinary differential equation systems
Fabio Botelho
Comments: 9 pages
Subjects: Numerical Analysis (math.NA)
10. arXiv:1712.02701 [pdf, ps, other]
A duality principle for non-linear elasticity
Fabio Botelho
Comments: 10 pages, more typos and errors corrected, some parts of the text have been re-written
Subjects: Optimization and Control (math.OC)
11. arXiv:1712.01595 [pdf, ps, other]
Global existence results and duality for non-linear models of plates and shells
Fabio Botelho
Comments: 28 pages, some parts of the text have been re-written, variational nature of the dual formulations retaken
Subjects: Analysis of PDEs (math.AP); Optimization and Control (math.OC)

This work is dedicated in memoriam to Professor J.J. Telega

12. arXiv:1712.01031 [pdf, ps, other]
On duality principles for non-convex variational models applied to a Ginzburg-Landau type equation
Fabio Botelho
Comments: 14 pages, more typos corrected
Subjects: Optimization and Control (math.OC)

Artigos completos publicados em periódicos


1. Fabio Botelho, A note on Riemannian geometry and the relativistic quantum mechanics context. CIÊNCIA E NATURA, v. 40, p. 58, 2018.


2. Fabio Botelho.,A Variational Formulation for the Relativistic Klein-Gordon Equation. CIÊNCIA E NATURA, v. 40, p. 57, 2018.


3. Fabio Botelho, On the Generalized Method of Lines Applied to Ginzburg-Landau Type Equations. International Journal of Applied and Computational Mathematics, v. 1, p. pp 1-15, 2016.


4. Lucas dos Santos Fernandez, Alexandre Molter, Fabio Silva Botelho, Simultaneous topology optimization and proportional actuators localization. SeMA Journal, v. 23, p. --, 2016.


5. Fabio Botelho, On the Lagrange multiplier theorem in Banach spaces. Matemática Aplicada e Computacional (Cessou em 1997. Cont. ISSN 1807-0302 Computational & Applied Mathematics) , v. 32, p. 135-144, 2013.


6. Fabio Botelho. Existence of solution for the Ginzburg Landau system, a related optimal control problem and its computation by the generalized method of lines. Applied Mathematics and Computation , v. 218, p. 11976-11989, 2012.


7. Fabio Botelho, On duality principles for scalar and vectorial multi-well variational problems. Nonlinear Analysis , v. 75, p. 1904-1918, 2012.


8. Fabio Botelho, Dual Variational Formulations for a Non-linear Model of Plates. JOURNAL OF CONVEX ANALYSIS , v. 17, p. 131-158, 2010.