Sumários

Distributions (I)

22 Outubro 2019, 10:00 Manuel Duque Pereira Monteiro Marques

Distributions: motivation and basic ideas. 

 Generalization of functions and derivatives: examples.
Test functions, distributions, convergences.


The wave equation (II)

18 Outubro 2019, 11:00 Manuel Duque Pereira Monteiro Marques

The homogeneous wave equation in R: d'Alembert's formula for the initial value problem, 

cone of dependence and stability.
The nonhomogeneous equation and Duhamel's principle.


The wave equation (I)

17 Outubro 2019, 11:00 Manuel Duque Pereira Monteiro Marques

Example (string) and uniqueness by the energy method.


The Heat/Diffusion equation (III)

15 Outubro 2019, 10:00 Manuel Duque Pereira Monteiro Marques

The fundamental solution: conclusion. 

The homogeneous problem: solution by convolution with the fundamental solution and the regularizing effect.
Reference to the non-homogeneous problem: uniqueness and existence (by integral superposition). 


The Heat/diffusion equation (II)

11 Outubro 2019, 11:00 Manuel Duque Pereira Monteiro Marques

The weak maximum principle and its consequences:

uniqueness, comparison, stability.
The search for a fundamental solution of the H/D equation: 
invariant transformations, conservation of mass.