Contents

(Veja a versão em português ).

Part 1. Introduction

1.1. Veja a Introdução em português

1.2. Credits

 

Part 2. Testimonials

2.1. In Memory of Daniel Bauman Henry (Dan)

2.2. A importância dos trabalhos do professor Daniel B. Henry

2.3. Some words in memory of Dan Henry

 

Part 3. Dan Henry´s Manuscripts

3.1. Lecture Notes

 

Evolution equation in Banach spaces

Chapter 1. Linear semigroups

Chapter 2. Mildly nonlinear equations

Chapter 3. Kato´s theory of linear and quasilinear equations

Appendix: The spaces

 

Partial Differential Equations

Chapter 1. Some introductory examples

Chapter 2. First order scalar equations

Chapter 3. General Cauchy problem

Chapter 4. Well-posed problems and others

Chapter 5. The wave equation | Appendix

Chapter 6. Other hiperbolic problems | Appendix

Chapter 7. Theory of trumpet

Chapter 8. The heat equation | Appendix

Chapter 9. Fourier transform methods

Chapter 10. Second order elliptic equations

Chapter 11. General elliptic systems

Chapter 12. Linear semigroups

Chapter 13. Linear evolution equation

Chapter 14. Local and micro-local theory of differential operators

 

Differential calculus in Banach space

Chapter 1. Continuity

Appendix 1: A brief review of metric space

Appendix 2: Teorema de extensão de Whitney

Appendix 3: O teorema de Sard

Chapter 2. Differentiability and analiticity

Chapter 3. Implicit functions and related notions

Chapter 4. Approximation bysmooth functions: partitions of unity

Chapter 5. Differentiable manifolds

Chapter 6. Transversality: theme and variations

 

Elliptic partial differential equations

Chapter 1. Laplace's equation | Miscellaneous exercises

Chapter 2. Second order elliptic equations

 

Órbitas homoclínicas para sistemas dinâmicos

Capítulo 1. Introdução: caso planar e ferradura de Smale

Capítulo 2. Variedade estável / instável

Capítulo 3. Dicotomias exponenciais

Capítulo 4. Conjuntos hiperbólicos: teorema de Smale

Capítulo 5. Perturbação de órbitas homoclínicas: o problema de Melnikov

Capítulo 6. Os problemas de Shilnikov

Apêndice: Sobre equações de evolução (semilinear)

 

3.2. Dated Research Notes

 

Simple Schauder (01/1981)

Why is wet sand darker than dry sand? (12/1982)

Exemplo de falha de unicidade (06/1983)

Funções quase periódicas (08/1983)

Mudança de variáveis por Séries de Lie (10/1983)

Gravitational field of a slightly spheroidal mass distribution by pertubation of domain (06/1983)

Por que o camelo é peludo e outros problemas de termobiologia (06/1986)

Derivation of the equations of linear thermoelasticity (06/1986)

The method of stationary phase with minimal smothness (06/1993)

Complete asymptotic expansion of (08/1993)

Useless facts about high-order derivatives of exp(-1/x) (02/1994)

Dichotomies, hiperbolic sets, shadowing lemma and chaos (11/1994)

Some topics in bifurcation theory (05/2000)

A simple Vander Monde é diferente de zero (genericamente) (05/2000)

The complete complex quadratic equation (10/2000)

The linear transport equation with applications (11/2000)

 

 

3.3. Undated Research Notes

 

Pseudo-differential operators

How to remember the Sobolev inequalities

Invariant manifolds near a fixed point

Some spectral theory

Local solutions of analytic matrix and operator equations

A difference equation

A equação funcional de Cauchy

A problem of Einar Hille

Exterior problems for the Helmholtz equation

Fredholm operators

Um caminho rápido através de Sacher e Sell: "Existence of dichotomies"

A singular gradient flow :

 

 

3.4. Handwritten version of the paper "Topics in Analysis" (published in Pub. Sec. Mat. Univ. Autònoma Barcelona , 31 (1987), no.1, 29-84)

 

Topics in analysis

1. Examples on propagation of singularities in the wave equation

2. Non-decay of thermoelastic vibrations in dimension ≥ 3

3. On some non-linear integral inequalities of Kielhöfer and Caffarelli

4. An example in the spectral theory of semigroups

5. A property of the exponential function

6. Asymptotic behavior of some scalar ODEs and an elementary example of non-minimal ω-limit sets

 

 

3.5. Science Fiction – by “Lor Martinelli”

 

Prolegomena to any future science ficction

Apology for science fiction

Let´s colonize the Galaxy

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