Fabio Silva Botelho, PhD

Professor Adjunto, Departamento de Matemática

Universidade Federal de Santa Catarina - UFSC



Cálculo Variacional


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


Atenção para o novo horário devido à colisão de horários


Terças 18 h – 20 h 30 min


e Quintas 16 h – 18 h 30 min


Sala CFM A 11 – Ambos os dias


Informe o Professor Fabio Botelho caso haja colisão de horários.




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


This is the correct , revised (submitted) version.

For some reason the Journal Ciência e Natura published a previous not revised version.

Also, for this article, the journal has indicated in its web-page:

Article received 04/12/2017 (day,month,year)

Article Accepted: 05/06/2018

For the other article published, they have indicated:

Article received: 04/08/2017

Article Accepted: 04/09/2018


Indeed these dates are not correct. The two articles I have published in this journal were both submitted about April/May 2018 and accepted

about 45 days after submission with a GAP of about 30 days between the acceptances.

Also, the journal did not present the proofs of both articles to the author for verification and final agreement.


Pre-prints-Applied Mathematics


1. arXiv:1902.08811 [pdf, ps, other]
A note on optimization in Rn
Fabio Botelho
Comments: 10 pages
Subjects: Optimization and Control (math.OC)

1. arXiv:1902.04448 [pdf, ps, other] (Parte da tese de mestrado de Eduardo Pandini sob a orientação de Fabio Botelho)
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)
6. 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

1. 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)
2. 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)
3. 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)
4. 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)
5. arXiv:1712.02701 [pdf, ps, other]
A duality principle for non-linear elasticity
Fabio Botelho
Comments: 10 pages, typos and erros corrected
Subjects: Optimization and Control (math.OC)
7. 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)