Sumários

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.

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.

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

Exercises: the wave equation, example and uniqueness

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).

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.