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

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


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: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.