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 (continued)

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.
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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.


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