Sumários

Evolution equations

20 Dezembro 2019, 11:00 • Manuel Duque Pereira Monteiro Marques

The wave equation (continued): existence of one solution, regularity.

Final comments: continuous semigroups of contractions.

Evolution equations.

19 Dezembro 2019, 11:00 • Manuel Duque Pereira Monteiro Marques

A model hyperbolic equation: the wave equation.

Formulation of the corresponding evolution problem. Conservation of energy.

Evolution equations.

17 Dezembro 2019, 10:00 • Manuel Duque Pereira Monteiro Marques

A model parabolic equation (the heat equation) as an evolution problem in a function space.

Maximal monotone operators. The Hille-Yosida theorem (without proof). Application to the heat equation. 

Eigenfunctions of the Laplace operator.

13 Dezembro 2019, 11:00 • Manuel Duque Pereira Monteiro Marques

Characterization of the first eigenvalue of the Laplace operator with homogeneous Dirichlet boundary condition.

The best Poincaré constant.

Eigenfunctions of the Laplace operator

12 Dezembro 2019, 11:00 • Manuel Duque Pereira Monteiro Marques

Eigenfunctions of the Laplace operator with homogeneous Dirichlet boundary condition.

Spectral decompositions of L^2 and H^1_0.